Lecture 5: Operators and the Schrödinger Equation

MIT 8.04 Quantum Physics I, Spring 2013
View the complete course: ocw.mit.edu/8-04S13
Instructor: Barton Zwiebach
In this lecture, Prof. Zwiebach gives a mathematical preliminary on operators. He then introduces postulates of quantum mechanics concerning observables and measurement. The last part of the lecture is devoted to the origins of the Schrödinger equation.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
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[@AdityaKumar-ij5ok]

The thumbnail really looks like he's fighting with QM

[@shrikrishnamishra2345]

:D yes

[@technicalstudyTEengineer]

Yes you are right

He’s standing face to face with the final boss

[@nirajsinghkarki2319]

🤣

[@samdades7216]

I really thought it was a meme or something lmao

[@meetghelani5222]

I've watched some lectures of Professor Zweibach's course on quantum mechanics and by what i can say, barton's and allan's combination is probably the best anyone can have in their lives for QM, thanks MIT OCW, love y'all for providing this!

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@everything_strength]

18:10 is an example of why this teacher is great. He doesn't just do some hand wavy crap or dismiss the question, but shows WHY on the black board. A teacher that can derive things from scratch is like GOLD

[@naught_]

it goes both ways. some of my physics professors waste all of the lecture showing derivations, which is kinda useless because my textbooks already have the derivations and making the concepts clear to understand are the part the book lacks. a good balance between conceptual explanation and derivations is what makes this man such a great teacher.

[@zack_120]

Yes, he backs up everything he said with proof or examples.

[@giacomocasartelli5503]

Except there he was actually wrong because the dirac delta is not a function, hence the multiplication makes no sense at all in his definition. That said, the dirac delta is indeed an operator (actually it is a tempered distribution or even more specifically a compactly supported distribution), but it is defined as follows: delta_a(f) = f(a). It just becomes the evaluation of the function in the point a. I think what he meant was the integral of the product he wrote. In that case we can use the fact that the linear functionals (aka distributions) act on test functions by integral product (usually the notation is similar to that of L^2 inner product, or in L^p-L^q product, which exists by Holder's inequality). The integral is well defined by at least one of the two being of compact support (or well behaved at infinity) and that's ok. (I'm intending operator as in general term, the image space is obviously the complex field, hence functional would be more precise) I think being able to derive things on the spot is the bare minimum that an expert should be able to do if he holds uni lectures. Unfortunately there he was caught a little off guard.

[@alancasallas1501]

The Hitchhiker's Guide to Quantum Mechanics.

[@frejadzougov7091]

Operator P42

[@quantumme9938]

Universe bless you MIT for making these invaluable lectures available to us. Thank you very much. My go to source for all my physics :)

[@Low_pH]

*god bless

[@dagkouta986]

i have literally spent around an entire week.end downloading ALL lecture videos, lecture notes, assignments, exams, etc... for almost all courses... worth my time

[@lugia8888]

@@dagkouta986 shut up

[@chaoxu7360]

never saw a professor was applauded at the end of the courses. but dr. zweibach certainly deserved this. the best lecture on this topic I have put myself in.

[@alfredowaltergutierrezmald834]

As a Peruvian, I feel proud of this genius!

[@NicolasSchmidMusic]

Are all the Professors at MIT so enthousiastic and smart?

[@bobbriggs4287]

I love listening to this professor. Even the hard stuff goes down easier with his friendly delivery.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@raihansyahharahap]

This is the best lecture that I ever seen and it free. You helped many peoples. Very Clear. Bless you MIT.

[@chrissch.9254]

I studied Quantum Mechanics more than 30 years ago - I wish I had had a lecturer like this one… 🙂

[@quynhle9938]

This is absolutely the PERFECT lecture for Schrodinger and I am so grateful for Dr. Z. He relates the math to the Physics, and makes sense of it all.. I need more :)

[@schmetterling4477]

Where did you see physics here?

[@hasanshirazi9535]

Eigen functions and Eigen values explained brilliantly.

[@codeme1529]

Wonderful! It was updated to the high quality! Finally!

[@DevinBost]

This was one of the most mind blowing lectures in physics I've ever seen.

[@TheThunder48]

So much thanks for this MIT team, i love physics but my professors just cant explain it!

[@abhishekravindra4008]

MIT professors are out of the world in explaining things making math speak out they are simply awesome

[@simpleandsuccess]

Wtf - this dude is so fluent its crazy. Love his style. Great teacher.

[@robertdowadams]

24:30-25:00, the explanation of eigenvectors that I'd have paid 80,000$ for.

[@AndrewSanchez11235]

I was just about to comment on the same thing. I've taken a full course of Linear Algebra but that explanation was better than anything i had in the LA course.

[@JRush374]

Check out 3blue1brown's playlist on linear algebra.

[@gaspardsagot628]

Boi that's just the definition really

[@walucanguro]

Dude, that's the definition... Av=λv

[@yfsfundocele344]

yeah it insane how he simplified it(not many people can explain eigen values,vectors,states)

[@altunhasanli]

Thank you, MIT, for the value you put in us - self-learners, also thank you, for those who donate and make these lectures available for us. Hope I'll be listening to these lectures live as a student of MIT. Good luck to me! (I guess)

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@imaseeker100]

masterful teacher.....and a substitute for another world class lecturer

[@rontoolsie]

Watching this a few times will eventually result a eureka moment of understanding not only how the Schrodinger equation works and can be derived, but also how it MUST be just so. It also takes the oft used term 'wave function collapse', and fleshes it out into how the measured observable (x, p or whatever) has to be an eigenvalue of the original wave equation, and it is modulated by an eigenfunction of the operator of choice. This lecture is presented with all the skill of a masterful prosecutor building up an unassailable case brick by brick, culimating with the 'got you'coupe de grace of crowning the E scalar value with its operative symbol, thereby unlocking the gateway to quantum wave mechanics. It is little wonder that the students give a warm round of applause at the end of this. But had they been able to fully digest the minutiae and nuances of this talk, it would have easily been a standing ovation. This is the quantum mechanics equivalent of the brilliant James Burke series of Connections from the BBC, or the equally as scholarly (but not quite so charismatic) Mechanical Universe presentations by David Goodstein from CIT.

[@Gwunderi25]

+Ron Toolsie Did I get the last "genius coup" at the end (1:19:30)? Does putting a hat on top of E mean to "force" the energy to be quantized, to take only certain discrete values (the eigenvalues)? And (consequently) the other "observables" too? And if yes: isn't also the uncertainty principle hidden in this equation?It's an excellent lecture and Prof. Zweibach should indeed get standing ovations. I saved the video twice to be sure ... : )

[@Darthvanger]

Thanks for the recommendations, I'm going to watch both of those episodes!

[@ahuhu]

This particular episode is just epic. And I can kind of feel Prof. Adams's disappointment not being able to introduce the Schrödinger Equation himself in all its glory, having been laying its foundation for the last four lectures.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@Deepakfly]

I studied quantum mechanics, from many different sources, But this is best one..... World's best!!!!! Thank you MIT And Dear Teacher.

[@brabantstad384]

I love to watch this, I dont understand much but its great lecture

[@dj098]

Amazing lecture. Well structured, clear and extremely engaging; it takes you on a journey where your knowledge and understanding of the topic progressively grows, but it's so balanced that it doesn't force anything on you.

[@schmetterling4477]

That is only halfway correct. The problem with non-relativistic QM is that it is not a proper physical theory, but that is usually not being explained to you while you are learning it. One should, for instance, tell the student that the Schroedinger equation does not conserve energy, momentum and angular momentum and that the projection operator formalism for measurement balances this out in just the right way to arrive at the correct physical results for the kinds of systems that can be described by non-relativistic theory to begin with. That entire background is usually missing from QM 101 lectures, including this one.

This topic it's so hard and abstract but the professor made it look so clear, thats definition of a Genius , one who makes complex things easy

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@ThabetMarwa]

Never saw someone explain Eigenvectors as greatly before ! 27.00

[@Saptarshi.Sarkar]

Watch 3B1B's video

[@zack_120]

27:00 - now click it.

[@Euquila]

neatly and enthusiastically presented. thank you!

[@aziahthomaz2496]

This gives new meaning to the song Smooth Operator by Sade

[@krisfalkenberg]

B23 The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky. When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser. So please Vote B23

[@AlanMedina314]

Excellent Lecture very clear. I have been going crazy trying to understand operators but this video really helped.

[@NazriB]

Lies again? Laundry Operator

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@dominicellis1867]

So the uncertainty of an operator is the standard deviation of that operator. It’s a measure of how spread out the probability density is from the maximum knowability or the mode of the pdf transformed by the operator.

[@palvindarchhokar9821]

Brilliantly given lecture, was really drawn in.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@amolive]

Excellent explanation.

[@Aaaaaaaaaaaaaamin]

What a beautiful lecture.

[@aeroscience9834]

47:57 mathematicians were the first to work with abstract linear operators and infinite dimensional vector spaces, so I don't think you're giving them enough credit. Mathematicians don't think in just matrices.

[@aeroscience9834]

However, it was an amazing lecture!

[@pettPette]

mathematics is the study of all patterns. Physics is basically concerned with patterns observable in this universe. Therefore, he made a little mistake there! Whatever, Physics discovers is within the realm of mathematics

[@patrickd5972]

I know this is a little old but I'll add: his description is probably what you'd get from an undergraduate math student, and it's a totally legitimate first attempt to try to understand the situation. If you showed it to a seasoned mathematician the response might depend on their specialty, but many would probably recognize right away that in finite dimensions commutators have trace zero. An analyst would be unfazed (operator algebras are a major part of the subject). An algebraist might tell you about the Weyl algebra, which is something that some might describe as slightly "pathological", but not really for the reason he describes (for one it is simple but not semisimple, a confusing conflict of terminology). Nevertheless, the Weyl algebra is well-studied so it's definitely not something that mathematicians shy away from.

[@zack_120]

Beautiful blackboard hand writing to say the least of this professor, Awesome MIT Professorship!!

[@SantosPerezAttorney]

I traveled in a timelike Geodesic, bent time, and got here super quick.

[@MistressGlowWorm]

Magnificent lecture.

[@zeotex2851]

i love the "professor kidnapped by pirates" subplot

[@andreagang5263]

still helpfull all these years later!

[@unrgisterdhypercam2]

thank you thank you thank you this helped me so much THANK YOU

[@elamvaluthis7268]

Very good explanation for an ordinary man a boon lecture thanks a lot for the professor.

[@saraharonson9720]

great work ! professor .

[@alfredowaltergutierrezmald834]

beautiful!

[@Poemand]

Thank you so much for this great lecture 👏❤

[@someoneelse2417]

He's a brilliant lecturer. Absolutely brilliant.

[@youtubeshortsviral1361]

1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@ArthurXandTheScars]

I love this lecture! Very clear and funny.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@technicalstudyTEengineer]

Really good explanation

[@galacticpizza5619]

I love the hitchhiker's guide to the galaxy reference

[@flinkwieeinwiesel5657]

The moment he said "I'm not gonna do that" I was immediately aware that this will be a tough ride :)

[@ErickFGx]

this helped me to put my ideas in order thanks for share

[@arielgamboavazquez4250]

high quality education as usual :)

[@hgtrad7655]

Very clear and interesting thank you.

[@dhanushka5]

finally someone actually like to teach

[@schmetterling4477]

He is very funny at 49:0 when he goes on about how mathematicians struggle with the most simple case of commutation. He is right... you can get an entire lecture called "functional analysis" about that problem and it's quite ingenious.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@abdulsattarkhan8670]

This was amazing lecture takes quantam mechanics to different dimension I can feel Prof Adams downcast on not able to introduce schorimder equation in it's full glory

[@youtubeshortsviral1361]

1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?

[@okaythisisepic3212]

I don't get why there's two energy operators, the short one @1:15:39 and two term one @1:20:20 ? In what context can each be used?

[@MusaHusseini]

Watching Mr. Barton Zwiebach's elegant explanation of deriving iħ ∂ψ/∂t = H^ψ (TDSE) and H^ψ = Eψ (TISE) is like going back in time to the first quarter of the 20th century and meeting one of the greatest minds in QM (Heisenberg in 1925 and Schrödinger in 1926), both of whom revolutionized physics with such cognitive cataclysm!

[@schmetterling4477]

Anybody who shows you a "derivation" of the Schroedinger equation is performing a parlor trick for you. It can't be properly derived from anything, if for no other reason than that it's completely wrong. At most one could argue that it's a non-relativistic perturbation solution for quantum field theory, but I am not sure it's even that (you can see this because it doesn't include the Pauli exclusion principle, for instance, which should not drop out in a proper perturbation theory).

[@agroumabderrahmane5199]

very nice movie, great explanation

[@youtubeshortsviral1361]

1:03:11 here a is the Eigen value right? And isn't modulas squared of Ca ie cofficient is the probability of getting one of the pure state, Instead of a?

[@BilelMnasri13]

Merci beaucoup MIT

[@thelonegerman2314]

I'm Interested in the DIAGAGNOLIZATION of matrix EIGENVECTORS, and VECTOR using Taylor expansion and DETERMINANT for infinite series and PAULI MATRIX and Clifford Algebra for solving the Schoringer Equation And HEINGBER uncertainty for QUANTUM FIELD PERBUTATION

[@MrMachi95]

good lecture, i'm a bit confused about there being 2 energy operators though...any insight?

[@user-cn4qb7nr2m]

As schroedinger`s eq tells us they are equal, it is basically the same operator in different forms.. Kind of like 1+4 and 2+3 is the same number.

[@davidwilkie9551]

A couple of SiFi stories have "pointed out" that the Universe is a point, ie the Temporal POV IS Singularity property, that is the Philosophers "indescribable" temporal superposition spin-spiral function cause-effect of time duration timing modulation, we are Totality embedded in.., but cannot describe because it's "No-thing", e-Pi-i omnidirectional-dimensional connection by Pi-bifurcation Exclusion Principle that "floats" numberness in macro-micro, divergence-convergent, Vanishing point-positioning, ..and is the pure-math Superspin-spiral pivot of here-now-forever localization circularity.., the Condensed Matter and Theoretical Quantum-fields Mechanism of AM-FM In-form-ation substantiation that is the subject of the lecture. (By default?) If the lecture starts as it should with "known physical empirical laws" then this is the hierarchical dominance of phase-locked coherence-cohesion probabilistic pure relative motion logarithmic pulse-evolution differentiates in potential mathematical motion, possibility.., an Equation of this particular Timing-spacing integration wave-particle coordination-identification. By default, the Quantum Operator Fields Modulation Positioning Computation Mechanism is the only Actuality, in projection-drawing Perspective, Principle.

[@TJ-hs1qm]

@12:09 I would have thought that the multiplication is the operator acting on a matrix and a vector. The latter one being the objects. Basically like this Mult(matrix, vector).

[@FocoEsportivoo]

at 1:00:10 them subtitles say 'Fourier told you you can't expand..." which is wrong (the professor didnt make that mistake, its only on subtitles); in fact Fourier 'told' us that we can expand any function as a linear combination of e^ikx.

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...

[@kazemvafaeian4980]

Very very good lecture. All the previous lectures was like isolat islands and focused to "draw attention to me I am hero" even the pirate theater target to the same. I think the fifth lecture by this gentlemen "great teacher" covered all the previous artistic plays. I think MIT may make a survey from different level of educated people like, those who know QM, familiar with QM or don´t know, to use the donated money on real lectures.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@magnfiyerlmoro3301]

Why is there the conjugate of the wave function in the beginning ? For p

[@zphuo]

@45:50, why x and p order matters means that when you measure one you have difficulties measuring the other?

[@non-inertialobserver946]

If you could measure them both like you would classically, then it shouldn't matter in which order you measure them.

[@krisfalkenberg]

B23 The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky. When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser. So please Vote B23

[@octaviorex244]

Drrrr this is so obvious X(f) is the function of the vector it's super clear, yeah I didn't whent to school but I find it fascinating

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...

[@hurtcolor]

35:07 energy operator V(x hat) ???? 55:00 energy collapses to eigenfunction psi_a 57:30 1:03:00 ?????? 1:12:00 ...... this is the operator that realizes the energy

[@dudebros6122]

Thumbnail goes hard af 🥵

[@ersanovo4308]

Isnt there a mistake at 35:35 ? Should be ... + x*v(x)*psi(x), no? (the x is missing)

[@ricardocesargomes7274]

Ótimas aulas!

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@onurcanbektas8411]

At 52:08, it is Hermition operators, not "permission".

[@JohnSmith-zq9mo]

As a mathematician who has worked with the Weyl algebra I found his comments about mathematicians amusing, and quite wrong. There are things that mathematicians find difficult to understand in quantum mechanics since it has not been made rigorous but the Heisenberg commutation relation is not one of them.

[@user-fb4zo8wd5n]

John Smith I think he was just teasing mathematicians. Of course, mathematicians work with infinite dimensional spaces and hold seminars on operator theory all the time. If it weren't for mathematicians, physics wouldn't be where it is today.

[@PDEblog]

He is just refering to the fact that the Heisenberg commutator requires the operators to be unbounded, the other one does not. This is what makes it more complicated.

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...

[@akhilife_t]

Best things of the universe are always hidden. They are not put up on advertisements boards or tv commercials. They are always discovered by keeping a meticulous perseverance. "Truth is not for all men but only for those who seek."- Ayn Rand Thank you Universe!

[@syzygy21cm]

Using the operator P42 ---> 42. Is this a reference to "The Hitchhikers Guide to The Universe" I wonder?

[@giacomocasartelli5503]

As a matematician I beg to differ on what the professor said about us wanting to compute finite dimensional matrices. I think the most elegant mathematics is that of the infinite dimensional spaces that are behind this kind of phisics. I'm not at all scared by the fact that we are considering normed (or semi-normed) TVS and their duals without exhibiting any finite-dimensional basis for them, as long as I understand the underlying uniform structures and rigorously define what equality in the dual space means (i.e. weak equality on the test function space).

[@schmetterling4477]

That's all cool, but you have to understand that physicists aren't giving a crap about any of that detail. For one thing we know that the SE is unphysical. It's a toy model that gets you exactly nowhere in real physics. For us the buck stops at the Dirac delta, which is the one line poor man's version of three hundred pages of functional analysis textbook. The stuff that we really care about (relativistic quantum field theory) is outside of the reach of serious mathematics for now as far as I know.

[@giacomocasartelli5503]

​@@schmetterling4477 Oh, then I misunderstood what he was saying. I tought he meant "scary" as if we wouldn't want to deal with it, since I actually find it fascinating and that's why I'm all about it; but he probably meant it in the sense that we need to build a coherent theory which is sound and compelling, whereas for phisicists is more about the actual meaning of those quantities in their model.

[@schmetterling4477]

@@giacomocasartelli5503 I also find functional analysis to be a fascinating mathematical discipline as it brings some sense of order into this infinite mess of functions. It just doesn't do much for physics because the problems with quantum mechanics do not stem from mathematical corner cases. They are deeply embedded in the core definitions of physics that all depend on a geometric substrate that we call "the physical vacuum". All our successes begin there, but so do all our failures. What needs to be exorcized is the notion of R^n as the underlying tangent space of reality. That's the end point and not the beginning, but for now we treat it as both and that's just wrong.

[@AdityaKumar-ij5ok]

1:01:42 watch with pause and subtitles

[@bensama7265]

Thanks a lot . I have a question : there are 2 energy operators !! One is the summation of the momentum and the potential operators , and the other is the one contains the partial time derivative !! Why :/ ?! I'm confused .

[@VerniasAugoeides]

Ben Sama The first is the time-independent Schrodinger equation, which just calculates the energy eigenvalues of the eigenstates; the system as a whole is time-invariant and states don't evolve with time(stationary states). The second is the time-dependent Schrodinger equation which shows​ the time evolution of the states of a wavefunction when you don't measure a system to make it undergo collapse.

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...

[@chivaswwe]

Uncertainty of the random variable "operator" is equal to its standard deviation (38:35)

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@benny4013]

perfect!

[@Harry-cs2zr]

This guy is actually even better than the other dude

[@krisfalkenberg]

B23 The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky. When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser. So please Vote B23

[@Guaulden]

There is an error in the subtitles at 18:12 that repeats. Not direct delta but Dirac delta.

[@mitocw]

Thanks for your comment! It's fixed now. :)

[@ChTL757]

MIT OpenCourseWare There is one more error at 52:02 . Not permission operators but hermitian operators.

[@pankajchoudhary8263]

I love wave function

[@CHistrue]

The build-up at the end is excellent! One question remains. He stated that Schrӧdinger Wave Equation is "deterministic." I cam cautious about accepting that but I would like to hear more about how it is deterministic.

[@breakfastenjoyer]

it's deterministically probabilistic :) lol

[@breakfastenjoyer]

More often than not, you'll get a range of answers but only that range of answers. It's deterministic in that sense.

[@CHistrue]

Mace Right, in other words, the probabilities are deterministic in the sense that waves on an ocean affect other waves in a certain pattern?

[@CrushOfSiel]

The wave equation has no physical meaning. It's only when you calculate the probability function that you get real world implications. The wave equation will give you this probability function exactly. But, yeah, the probability function will never give you an exact answer as to the properties of a particle at a certain time. That is what I'm to understand anyway...

[@CHistrue]

CrushOfSiel OK, but the wave equation describes the mathematics of momentum of the photon while the particle is the math of position. What it "really" is there is no one answer at this point.

[@frejadzougov7091]

In the last video a guess was made that =∫lΨ(x) l^2·p(x)·dx. In this video, p(x) has been cleverly replaced, but lΨ(x) l^2 has also been changed to Ψ*(x). Does anyone know why? As far as I see it a complex number times it conjugate would give us lΨ(x) l^2, når just the conjugate alone.

[@krisfalkenberg]

Taxes go up when they aren't cleaning up the debt product and garbage, an educating or protecting the country. Where they aren't going, the taxes are supporting its statue, host and image and drying up the land. Why we have states that will take refugees and the independent, that capitalism works, where people can have preservation and no walls can entrap. Stars shine bright mindful of others full of consciousness and life, rich of energy and power; "A people power" that can't be denied. Deny not the truth and receive. Where states only work and profit empowering the individual. State soul consciousness and have state of power. The conscience intellect survive. Principles bring down taxes and walls that hold servants of tyrants that exploit its public for its pleasures , while currencies fluctuate with emotions , commodities and consumption are following with out reason (intellect); Weather Taxing.

[@harshitagarwal5188]

at 39.0, what is tn=he logic behind those expectation value?

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...

[@Daniel-ws9qu]

I think the student meant his question about the delta function being an operator in a different way. Hes asked himself whether it even makes sense to multiply anything f with the delta function.

[@schmetterling4477]

Yes, one can multiply smooth test functions with the delta function just fine. The mathematical difficulties that arise in non-relativistic quantum mechanics are only pathological from an exact math perspective. They are not actual physical problems. It gets much, much worse in relativist quantum field theory where divergences are NOT caused by poor use of mathematics. They are the results of real physical phenomena and they have to be dealt with accordingly by using proper physical intuition about why they arise and how one can still extract useful phenomenological results from the formalism despite them.

[@FC-se8wf]

One word: WOW!

[@FamSisher]

Just popped in to comment on that absolute POWER STANCE in the thumbnail. Cheers.

[@krisfalkenberg]

B23 The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky. When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser. So please Vote B23

[@bobjones5869]

8:31 why is expected value of p depended on the conjugate of wafefunction, shouldn’t it just be based on the wave function itself

[@KutuluMike]

The expected value of p is based on the _square_ of the wavefunction, but since that is a complex function, to square it you multiply it by it's complex conjugate.

[@krisfalkenberg]

B23 The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky. When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser. So please Vote B23

[@dragonemperor007]

The description got the professor's name wrong. He is Prof. Zwiebach, not Prof. Zweibach!

[@mitocw]

Nice catch! You are the first person to notice and mention it in 6 years!! We've updated the descriptions (Lecture 8 was also wrong).

[@battlewing221]

there is also another version of 8.04 taught by Allan Adams, you guys can try him if you don't understand barton zwiebach

[@user-eb4fc5wg2i]

Do you have the link? I can't find it.

[@battlewing221]

@@user-eb4fc5wg2i yes sure kzbin.info/aero/PLyQSN7X0ro21XsVfRHhiWGEEJigdjpF3s

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...

[@prn718]

MIT: where your substitute teacher just happens to be one of planet Earth's leading minds in String Theory

[@bernandb7478]

at 2:20 I think it should be P(dx) = |Phi(x)|^2 *dx, since P(x)dx would be 0.

[@lsbrother]

No, P(dx) would be meaningless. P(x) is the probability density at the point x - an ordinary function of x. The integral of P(x)dx over all x must = 1.

[@kemalm9383]

SE... You can tell the energy where it's at ( located )....

[@back81192]

I have one problem. Think about position, for example, everytime we measure an object, we get the same result. If the result that we measured is eigenvalue, why we always get the same result? (Does that mean that eigenvalue is unique?)

[@gamerdio2503]

After the wave function collapses to a value a, you end up with AΨ = aΨ, in other words, after the wave function collapses, the measured value becomes the only eigenvalue. Any other eigenvalues before the collapse are now gone

[@krisfalkenberg]

Savings account Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place. Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...