Lecture 3: The Wave Function

[@anthonybrakus5280]

Big up to MIT for offering these OCW lectures. I have learned Calculus, Classic Physics, Linear and Abstract Algebra, and Quantum Physics and I didn't even have to pay late library book fees. 👍🏾 Thanks MIT, for being conscientious and gracious! 🎉💥🪅🎇🤸🏽‍♂️🕺🏿💃🏼🎆🎊🙏🏾

[@priscillacharlot8188]

Amazing !

[@ashlynparrott7130]

Fell asleep watching a ghost hunting video, woke up and this was on my TV thanks to autoplay. I didn't even feel groggy waking up because I was so alarmed by how good of a teacher this guy is. I'm more of a molecular biology person but I think I'll continue watching these!

[@AlexTrusk91]

i think this kind of high quality content makes the world a better place for seekers.

[@stauffap]

First you need to find it though. If you haven't figured out the value of science and scientific institutions yet you might end up "learning" "quantum mechanics" from "what the bleep" or Deepak Chopra, instead of learning it from MIT. The truth seems to be, that for many people it's hard to get on the right track without some type of guidance. They'll get sidetracked by conspiracy theories, fraudulent claims and various pseudo-sciences. And that may be understandable, since we haven't evolved to perceive or understand reality accurately. Furthermore our success (as a species) seems to be largely based on an accumulation of knowledge i.e. learning from other people and building upon that. So it's understandable that people can not see the value of the scientific method or scientific institutions. Scientific thinking isn't something, that has come naturally to us. It's not something that people just come up with themselves. So for most people it requires a person, who introduces them to science, leads them into the right direction, makes them ask the right questions etc. If you lack that you might not be very likely to end up here.

[@jacobvandijk6525]

You obviously missed this: 53:13. Think about it.

[@AlexTrusk91]

@@stauffap 4 years after my comment I'm not really any further with this lecture series. But started multiple other lectures on different topics like Human Behavioural Biology from Stanford. I'm also thinking of finally trythe problem sets, but I guess I maybe would be hit by a wall then. So I probably gonna try it anyways.

[@stauffap]

@@AlexTrusk91 You should definately try problem sets. You never fully understand physics if you can't do the math (you might just have the illusion that you understand it). I meet people all the time, who think that they understand a certain topic in physics, because they have developped a more or less accurate intuition, but they fail when confronted with having to calculate something and often fail as well with their intution. The ultimate test to whether or not you understand a certain topic in physics is always doing problem sets that involve math (and preferably understanding the derivations).

[@Abhi-mt4dn]

@@stauffap And can you help me abt problem sets like from where and how i should start to solve them like pre requisites and everything , i would really appreciate it

[@willcatch]

Whoever filmed this did a great job. Panning and framing. Spot on.

[@scowell]

Would have been nice to see his laptop screen as direct instead of through the projector... still, a wonderful job as you said.

[@Darthvanger]

@@scowell wow wow, we're not talking about THAT much advanced technology here.

[@mahinvasavada2992]

A class that ends with an applause. That is how all classes should be.

[@TheGersonfialho]

Not at all! Only professors with good didacts as this one deserve applauses!

[@kingplunger1]

@@TheGersonfialho Pretty sure the implication was that classes are supposed to be so good as to warrant applause

[@mishvanzant]

I love watching him lecture! He's so excited to show everyone "here's everything we've figured out so far, come help us figure out more!"

[@aussiedog5221]

Six years ago, after I retired, I went through these lectures and the second semester with Dr. Zwiebach. Simply outstanding. I am back for a bit of review. Thanks Dr. Adams and Dr. Zwiebach.

[@josephhall5681]

;Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.😢hh O❤ ❤❤❤

[@lukelively4732]

I wish I took school more seriously as a kid so I could go to this school. This professor is amazing and I love his passion.

[@bogdantokarski2798]

So do I.

[@softwareminimalist]

Yeah, you can learn now.

[@Darthvanger]

I've seen a few other lectures from the other teachers and I didn't like them as much as these ones. I think this is a gem, and we should appreciate we can watch the best of the best for free. It's not limited to the 100 of the smartest hardworking kids anymore and it's awesome!

[@mississippijohnfahey7175]

This is better though. All the learning with none of the crippling loans, egotistical teachers, or crushing deadlines! Einstein figured out SR while working as a patent clerk (though he did have a decent undergrad education)

[@RaidenShogun1145]

You can always work harder now.

[@weechinghwa8440]

Teaching in MIT is like a superstar singing on stage. Everyone claps for the good performance.. Holy moly

[@Tikorous]

People get excited when I stop speaking too, probably for a different reason

[@annehinrichs22]

Oh my goood, how can this be so much better than at my university?? The whole structure and order in which this is taught are just so clear!!

[@Ne012]

MIT is a very prestigious university. Very low acceptance rate because they take the cream of the crop in student's. If they do that for their students you can only imagine how they select their professors.

[@patinho5589]

@@Ne012 yeah but : I went to Cambridge.. very selective on students.. terrible lecturing and teaching in general in the subject I studied which was economics.

[@justindamirgian5977]

They put him in camera for a reason. I imagine they have good and bad professors also

[@whelan4545]

love this guys passion

[@r58302]

An absolutely perfect lecturer

[@paulboro5278]

You are my favorite teacher. I watched these lectures for the first time about four years ago. Because of these lectures, I have a very good understanding of basic quantum mechanics. I just completed my post-graduation from IIT Guwahati recently. These lectures were very helpful during the last four years.

[@IndrajitSen_TxState]

Truth be told, your IIT professors must learn pedagogy from these professors.

[@paulboro5278]

@itchy armpits I majored in physics.

[@theawantikamishra]

Engineering Physics?

[@MadScientist267]

I'm never going to directly use any of this but that hasn't kept me from trying to just understand it for my own curiosity. Never know when something will appear at the edges of something else and come in handy. This dude has come the closest so far to getting me there 🤣

[@josephflynn9560]

I love this so much. Trying to decide on Electrical Engineering or Physics. Did a long stint with the Marines and now using G.I. bill at a wonderful community college for freshman year. I have not been in school for a long time lol. MIT is still a dream and it feels SO good to be able to just listen. Watching these videos let's me know that I AM smart enough to sit here, even if life may not allow it right now. To be able to touch my mind to something I have wanted since I was a child is a gift and I wanted to say thank you to MIT and Prof Adams for doing this. One day, even if I am retired, I will take a degree at MIT , so stay awesome!!!!

[@yorichixX]

i did bachelors in electrical engineering now i am going to switch to masters in physics!

[@maxwellpineiro]

How is it all going ?

[@2Worlds_and_InBetween]

I was the kid at school who said I wanted to be a Physicist when I grow up... (... grow up.... something I might get round to one day ;-) and got told, "there's no point we already know everything" by the _teacher_ I went on to do mechanical and computer engineering with Physics /QM as the stuff I do for fun. but its more just a love of learning stuff do what you enjoy

[@jorgecastro5834]

I love the way the teacher brings those abstract postulates to live. In so doing he makes quantum mechanics crystal clear. He does it so well that one can not help feeling that there can't be a better way to put it (and I have thought about it several times). This work is invaluable! Just brilliant.

[@paulmuindiwilliam2945]

I'm somewhere in Kenya, and learnt about quantum computers, and I was curious. so I came across this lecture, and if i dont understand something I google it.. then i get another angle of understanding. i walk out of my house and look at the people and my relatives, i tell them about the beauty of quantum mechanics, and they just look at me like, do you have anything else to talk about, I'm like quantum computers will redefine the world as we know it... i'm just trying to understand where all this is coming from, how did they build that thing, what is the theory about it, what materials are used, where do they get them, how do they figure out the temperatures, how do they achieve that, how do they operate the thing.... well i guess it starts here, or somewhere close to here... so I'll keep on watching, going away to process everything, then come again the next day for more. this is heaven on earth!!!!!!!

[@ams1749]

I have my class 11 English language exam tomorrow, and here I am at 10 pm learning about wave functions,(this lecture is amazing and addictive though).

[@nc-broadcast]

Absolutely in awe at what Dr. Adams can do with just whiteboard and chalk. In another life perhaps I'd be in that classroom, or better yet in another world, following the Many Worlds interpretation of this beautiful subject.

[@olekbeluga314]

These lectures were very helpful in turning my room into a physics laboratory as I attempt to re-create the Hitachi experiment using homebrewed CRTs. It was not, however, all that helpful in subsiding my extreme existential terror. I'm going to be seeing things that go through neither both holes, nor one of the holes, nor none of the holes in my nightmares now. Thanks a lot, guys.

[@schmetterling4477]

Here, kid, have a cookie. :-)

[@marcostala]

I studied Telecommunications engineering. And now I realized that I was not that far to be studying formulas to be applied to Quantum mechanics. I mean, all these mathematical functions of waves are almost the same. Of course it helps that I was reading and watching lots of videos about the "double slit experiment" and such, to know what are you talking about. But I never expected I would understand so much about Mathematics of the Quantum Mechanics. It is all about Waves.... This concept of uncertainty (given by waves) is driving me crazy (in a good way) This is the first Quantum Mechanics Lesson that I can "somehow" follow! Thank You!! Amazing Professor!!!

[@victorfergn]

Physicists always try to use the same math, it was the kind of math especially designed for them.

[@ginnyjollykidd]

The concepts are easier to understand when you know the language, like psi and B*B

[@maurocruz1824]

{X,P}= complete knowledge. Postulate 1: Wave function. Postulate 2: The wave function is a kind of 'generator function' of the probability that the particle actually be in certain x position. 26:30 Postulate 3: The states of the system are closed under linear combinations. Mathematica package. Fourier transform.

[@jesse2450]

I wish there was a KZbin channel with instructors who are obviously super interested in the topic they are teaching regardless of the subject

[@FreshBeatles]

Great lecture. Can't wait for the free pizza at 5!

[@Andrewtmcb]

LMAO!!! xD

[@NovaWarrior77]

Dang. I missed it by 3 years...

[@putzak]

The pizza is an imaginary component probably

[@josef596]

@@NovaWarrior77 - I missed it by 4.

[@bzboii]

Wait it said free pizza at 5, not at 120…?

[@dooterino]

9:32 When he realizes how long we've been working on quantum theory he looks like a father proud of his son's progress. If I weren't dedicated to applying physics in the more esoteric corners of computer engineering that moment alone would have pushed me into pure physics.

[@brandonklein1]

High school senior here, I'm actually fascinated with that EXACT field!

[@nkeny1307]

Watching these for fun. What a great professor!

[@alexbillingham9593]

same. its completely irrelevant to my school work but its just so damn interesting

[@financewithsom485]

Watching before 1 day of exams

[@ismaelmelendez2710]

SOMMAN EDU did you pass? Are you now a quantum theorist

[@roku6194]

@@financewithsom485 how did they go

[@financewithsom485]

@@roku6194i am a software engineer now studied mechanical engineering that time this comment is 4 years back 😂

[@IliaToli]

You guys are too awesome. I finally start understanding quantum mechanics. I am a mathematician, chemist and aerospace engineer, but not a physicist. It is particularly hard to explain quantum mechanics to me, but you are outstanding. Will write my PhD thesis in quantum chemistry, which means that I can't have enough of quantum mechanics.

[@JimBob1937]

Ken, that's an odd statement. Obviously, in context, he is stating that a level of comprehension has personally been reached by him with enough confidence to state he is 'understanding' the current level of knowledge we hold. Obviously he isn't stating he's reached a mastery level of understanding that entirely exceeds that of all humankind to date... that would be a large assertion indeed.

[@ginnyjollykidd]

Quantum chemistry sounds awesome!

[@NazriB]

Lies again? WTF WOF

[@edwardhayes1314]

The teacher and course lecture is awesome, very professional. excellent job

[@Ztingjammer]

Came to his first lecture thanks to 3B1B, and here I am intending to go through as much as I can from Allan Adams ❣

[@learning4951]

In which video did he refer to allan?

[@sandipchakraborty184]

MIT is the only great source of quality education which is accessible to all.Thanks really i am greatly thankful to mit for giving the world a opportunity to become capable.

[@tanvec]

11:54 "Happy electrons" this guy is the Bob Ross of Quantum

[@occhams1]

I liked the StrongBad reference at 40:02 :) very subtle.

[@isaacmchugh6384]

This is the best TV show I've ever watched

[@mohammadkhalili3247]

your lecture is captivating, dear Allan! especially about superposition concept, i always just notice to math rule, but it has interesting physical meaning.

[@nickb4302]

It's amazing how accurate certain aspects of quantum mechanics can be calculated. They're basically just determining odds and they still get the right answer based on experiment. Weird.

[@dadestor]

Let me sound smart and say that is empirical knowledge 😌

[@santiagoarce5672]

Man, I love this lecturer! He's so enthusiastic!

[@JohnVKaravitis]

58:54 VERY slick teachable moment here. THIS shows that this guy knows his shit and gives a damn that the students can see how things connect.

[@MrsBreeFree]

Really cool lecture! I am from germany and go to University here, but your Profs seems really excited to teach and he makes fun jokes, its so easy to listen to him :)

[@AJ5]

I study at a Fachhochschule and yet I'm here watching these videos instead

[@christofchaos]

@1:00:12 Localized particles have less localized momentum because the momenta of the composite waves are cancelling and interfering with each other. Likewise, applying energy to the particles packet of waves causes the particle to move, albeit with some uncertain probability as to the direction/speed of movement. This movement reduces the coherence of the particle, and we become less certain as to where it is located. What is being described is the movement of a particle through space, but only if the particle is a secondary reaction created by the interfering waves. Try to imagine the amount of waves (EM or otherwise) passing through us at any second. Now imagine these waves all form the standing particles that make us up. They are highly localized, and their individual momenta are uncertain. But when we apply a macro-force to the system, the momenta of all these particles becomes more certain, and they become less coherent in the static, localized positions they were in before. As the waves re-settle, they regroup, becoming coherent again with all the particles being reformed in a different place and once again, localized.

[@ankitdedhia8460]

brilliant

[@MrMachi95]

play ride of the Valkyrie when he asks for it, fits beautifully.

[@tempestvideos9834]

In his mind the epic depth of what he is teaching is the objective gospel. Flight of the Valkyries... Passionate dude.

[@daveconerly1450]

This was one of my professors at MIT a while back. The class was exremely hard. He was a genius of course. . He talked pretty fast when teaching. . If for any reason you got behind , it was almost impossible to catch up.

[@karabomothupi9759]

Did you graduate?

[@zevikan8638]

proved to be a major help in understanding the uncertainty principle : )

[@kehaarable]

but how can you be sure?

[@anyuru]

38:30 "This is what quantum mechanics is all about" *pulls down board and shows "Free Pizza"*

[@Mohamedkassr]

Prof.John Admis, I couldn't express my thanks for your awesome lecture. Wave fns / Fourier series and transform notes. Also you're ready to any questions. Thanks :) for all things

[@CHistrue]

Some favorites: "Schrodinger's Cat, Wanted Dead And Alive" "Heisenberg Might Have Slept Here." And my own awful addition: "Mathematicians consider it risque when infinities cancel. Physicists are more tolerant. They do not mind if it happens during energy jumps as long as it is discrete!" Thumb this up if it is not completely horrible. My humor might have to be renormalized!

[@nachik09]

This is awesome!

[@CHistrue]

Nachiketa Ramesh Here is one not directly related to quantum physics, but reasonably funny none the less: "Entropy---It may not be the first bad law to keep a good man down but it is definitely the Second!"

[@nachik09]

CHistrue I didn't get this one. Second law of thermodynamics right? What man? How did it keep him down X(

[@CHistrue]

Nachiketa Ramesh Well, you know, it ruins the perfect closed system. No perpetual motion machines. I guess if I have to explain it, the humor misses. Should I try again?

[@nachik09]

CHistrue Yes please!!

[@biohazard5702]

At 9:30 he just realized how crazy this science is at what he is teaching and the enormous exponential Research and knowledge we gain and how fast we went from X to y in such a small space of time

[@biohazard5702]

I think he has add or ADHD cause I am the same when I look and notice what's Ian saying " I'am like dude whaooooo are your even realizing what you're saying"

[@xazau-]

This guy is good! A lot better than any of the physics classes I took!

[@nanoprehistoric]

17:30 the moment i realized that he wrote his own name as a wave function! Hahaha

[@Ne012]

So thankful now of all the hard work I put into Fourier series and transforms and convolution that I can do these problem sets.

[@RunuJena-me6zz]

At 32:23 he says that the momentum of the particle for the given wavefunction is p = (h_bar)(wave number) = h/(wavelength of the wavefunction) but shouldn't its momentum be h/(wavelength of the particle).Are (wavelength of the wavefunction) and (wavelength of the particle) the same thing and what does (wavelength of the wavefunction) mean?

[@schmetterling4477]

There are no particles in quantum mechanics. That's just the worst misnomer in all of physics. There are quanta. Quanta are combinations of energy, momentum, angular momentum and charge (electric charge, lepton number etc.). These system properties get exchanged from one system to another. Take a system with one charge, massive quantum, i.e. an electron. That's about as complicated a system as we can describe with this level of quantum mechanics. A single electron, on detection, gives us only one energy and momentum value. Imagine therefor an infinite repetition of that electron. That's called a quantum mechanical ensemble. The wave function of the quantum mechanical ensemble for one defined energy and momentum value can be described by a plane wave and that ABSTRACT plane wave has a wavelength. We can recover this wavelength in scattering experiments (many electrons scattering on a crystal lattice, for instance) physically. For a single electron that wavelength is not defined. Why? Because a single quantum doesn't give us an energy/momentum spectrum. We can't predict from just one measurement what the next measurement will give us. In order to measure that spectrum we need many quanta.

[@Innovativemediaandproductdesig]

This is the one subject that still holds my attention.

[@jordaneleniak]

I paused the video and started Ride of the Valkyries for the III postulate. Definitely added something to it.

[@hurtcolor]

43:00, 51:00, 1:00:00 (why are we uncertain about the momentum?), 1:02:00 amplitude !!, 1:12:00 fourier analysis…

[@schmetterling4477]

We aren't uncertain about momentum. Momentum is locally conserved.

[@jagergaming2281]

when the wavefunction is your signature

[@jandejongh]

Thanks Prof. Adams; absolutely brilliant intro into QM (not that I would know, I'm EE :-)). But just in case viewers need a perhaps equally well-taught lecture series on Fourier: There's an excellent treatment on this topic by Brad Osgood from Stanford available on YT. Highly recommendend!

[@cademosley4886]

Now that KZbin provides an overlay graph of the most watched parts of the videos when you hover the mouse over the timeline, I find it pleasing that that graph has two peaks, a smaller peak at 6:25 and a larger peak at 36:37. Remind you of anything? =)

[@thewaytruthandlife]

13:20 dX*dp >= h-bar shows us just how non localised matter is. from that moment on that this was written down it should have been understood that matter behaves non local .....in contrast to what classical physics states/shows

[@jackgude3969]

1:17:08 - I love how happy he is as he says "It's got uranium in it!"

[@TheDiabolocraft]

I had quantum physics classes in 2018 taught by some brilliant nutter who couldn't teach a class to save his life... Smart but just terrible. What a great time it was

[@Innovativemediaandproductdesig]

41:33 both sides of the equation are superposition in gravitational contraction

[@ogradus]

1:17:00 I think the Geiger counter messed with the camera and microphone for a second based off the angle of that plate while you were reading it. Cool!

[@BandhanGoyal]

At 59:53 - there need not be a wavelength for a momentum (unless we are presuming it a wave beforehand). E.g. A cyclist riding a bike has a momentum but no wavelength. Please clarify.

[@artistpw]

Really love the content available on youtube.

[@cbk41]

Dr. Benedict Gross from Harvard stated in his Abstract Algebra lectures that you could never know enough linear algebra. Seems like the big point of the decomposition of wave functions into their linear combinations and superposition helps to illustrate both of their points.

[@nemethma]

20 years ago I had these same types of classes. No clue what was going on at the time. Now I get it. Maybe can go get that A I was looking for!

[@Anomander888]

This man is so funny . Creativity is intelligence having fun in motion right here .

[@therealrictuar]

52:40 dont the cross terms have different signs because the norm squared is complex conjugate*function? so we end up with e^(i(b-a))+e^(i(a-b)), which is actually the sum of cosins? so we get cos(b-a)+cos(a-b)? so one might expect something that looks like big small small repeating?

[@RyanDeGreg]

7:00 he uses the word 'parsimonious' which means stingy and unwilling to spend money. I think he means to use the word 'harmonious.'

[@frede1905]

There's something I don't understand: I've learned that quantum wave functions can be described as a "ket vector" in an abstract vector space called Hilbert space. The position wave function, for example, used to express the probability of finding the particle at a point, can be described as a vector in an infinite dimensional Hilbert space. But we also have the wave function used to describe spin ("spinor"), and this wave function exists in a 2-dimensional Hilbert space. So my question is, what is the relationship between these two different wave functions? I've also heard that the wave function contains everything that there is to know about the particle, but I'm like, "which wave function 😭😧?" I would be really thankful if someone could help!

[@paulryan94]

The spatial wave function in the Schrodinger picture, psi, is not the same as a ket vector, | psi >. psi is the projection of |psi> onto the position basis: psi = < x | psi > | psi > holds all the information of the general quantum state and can be projected onto different basis's. That's why it's so useful. For example the momentum wave function can be arrived at by projecting | psi > onto the momentum basis: psi = < p | psi > But if you had just psi, the 'wave function', you still have a full picture of the quantum state because you can go to the ket | psi > from it.

[@frede1905]

@@paulryan94 Thank you for your answer, but the question I asked above was answered on physics stack exchange right after I made my comment. So it's no longer something that confuses me :). Here's the link to the question and answer on the site, if you're interested: physics.stackexchange.com/questions/560132/wave-function-as-a-ket-vector-in-a-hilbert-space

[@MrBoxinaboxinabox]

Was that a homestar runner reference at 40:00?

[@teammoof]

Yes it was. Nice catch.

[@domainofscience]

Haha yes it was! I wondered the same thing. Where are the consummate V's?

[@Taricus]

Nope. It's a dramatic orchestral piece. He means it'd make it seem epic while he lays down the postulate.

[@HighestRank]

Unlikely, though it probably was, depending on your prior ecology.

[@fredsolo730]

30:50 The stupid one is not a function but a relation by definition as a function can't be multiple valued Is that the reason why it can't be a wave function?

[@0xaugustus]

Are the recitation videos available? Thanks

[@oldfire3107]

At 35:25 when he explains about the doubt that the student had, he talked about light waves superposing, but isn't light wave function always real. Is there an example of a complex wave function for photons?

[@aidanstanford6742]

I honestly don't know an exact answer to this question as I have not researched it enough. If I had to guess I could say that any real function can be thought of as the real part of a complex function. Therefore there could be a complex function for a photon. It would also not hold up intuitively if not every particle's state could be explained with a complex psi.

[@jaurandt]

The answer to your question is that no quantum wave function is ever completely real. Wavefunctions are complex, always. If you are referring to real "light waves" as described by Maxwell's equations, those are not a proper description of "light" as it apparently works in reality. If I'm wrong, someone can let me know.

[@JaredAllegretta]

Exactly 40:00 - a very subtle homestar runner reference.

[@dalenassar9152]

@ timestamp 8:05, the proper pronunciation (of De Broglie) is DEE-BROY. Rhymes with LEE ROY.

[@psharmacgk]

Welp that settles it, I definitely wanna be a physics major

[@davidnovosardian6848]

No Name Sharma Really?

[@psharmacgk]

Yes! This was so cool :-)

[@joseph9589]

+dubhad Physics major here - actually, there is a 1% unemployment amongst physics majors, unlike the 49% among business majors.

[@ahadicow]

+Joseph Godoy that's probably because 99% of physics majors don't want a job.

[@joseph9589]

+ahadicow No, quite the opposite. The 99% do have jobs, either in mathematics, physics, or sometimes on wall street or in business.

[@LeonardGimson-zf7ry]

Very great professor, very interesting way to teach

[@peterjones7886]

Students can see other boards and digest the material in their speed. Videos presented here shows only the current positions of events; not pedagogically best practice. But lecturer is awesome. Thanks.

[@ximecreature]

+Peter Jones Well, you can pause, which a student can't do. Seeing the board you are taking notes from getting rolled behind another one is especially frustrating, if I could pause in the actual lecture room, it would be very nice. Being able to follow MIT lectures from home AND be able to pause to take notes properly is close to divine to me

[@david203]

If there are two peaks in an otherwise zero wavefunction (just before 46:24), yes you can say that on average the position is between the peaks. But each measured position can only be at one of the peaks, not between them. This is like saying the average side of a tossed coin is in between head and tail: it is not literally true. In fact, I would say it is misleading to talk about an average value when the data points are all in only two or three specific places. "Average" implies that data tends to occur near the average value, at least in English descriptions. If we are talking about Normal Distributions, then 'average" (mean) has a very specific meaning, of course. But two peaks are not a normal distribution.

[@tanyadeeedmondson-wl7vi]

Thank you all so very much.

[@JoeyFknD]

Ugh as someone with a math degree, I have paaaain imagining the problem he just casually tossed out: show why the wave function must be continuous. THANK GOD it's just in one dimension as well.

[@GalibFida]

Should I have studied Complex Analysis before studying this because I'm not getting how he got the norm squared of the linear combination of Psi_1 & Psi_2 @47:28

[@jamsque]

This got me too, I went down a long rabbit hole trying to figure it out but it is fairly straightforward, he skips a step that makes it a bit more obvious. The only thing you need to know from complex numbers is that |x|^2 = xx*, which you can see if you expand (a + bi)(a - bi). The cross terms cancel, leaving you with a^2 + b^2, which is the definition of |x|^2 because pythagoras. The skep he skips is to use this definition to first expand |aPsi_1 + bPsi_2|^2 into (aPsi_1 + bPsi_2)(aPsi_1 + bPsi_2)* Complex conjugation distributes (aPsi_1 + bPsi_2)(a*Psi_1* + b*Psi_2*) Now we multiply aa*Psi_1Psi_1* + bb*Psi_2Psi2* + a*Psi_1*bPsi_2 + aPsi_1b*Psi_2* In the expansion in the lecture he converts the first two terms back into norm squared notation to highlight the similarity with the component wave functions |a|^2|Psi_1|^2 + |b|^2|Psi_2|^2 + a*Psi_1*bPsi_2 + aPsi_1b*Psi_2*

[@resistance7538]

2 years from now I'll be sitting in that class...

[@JohnSmith-gh7br]

1 more year!

[@deepserket4390]

covid-19 goes brrrrrrrr

[@karabomothupi9759]

@@deepserket4390 😂😂😂

[@usptact]

Quantum physicist pickup line: your wave function is so beautiful.

[@rajns8643]

Really amazing

[@otterhead10]

16:12 “You should never forget that the wave function is complex” boy you can say that again!

[@squeevey]

Did professor just make a strong bad reference at 40:02? (The system -is down)

[@nomad9518]

Wow, they applauded for the guy. Well deserved.

[@sameertomar5099]

One of the best Professors

[@breaker4312]

I followed the first episode 100%. Then I plummeted :(

[@JimBob1937]

Yeah, the first lecture is covering an intuitive understanding and developing a platform before introducing the mathematics. However, you can only progress so far before introducing that portion is required. However, MIT OCW has the prereqs on their site I'm sure.

[@ankeunruh7364]

@Eric R, try the second lesson again! We, who are watching here on youtube, aren't MIT students. I can sware, that mathematics (esp. calculus) has been taught to us for centuries as it was an enemy. We need to fight for better teaching!! Those Professors must work on this!! They must try their very best, and I think most of them will fail (as I can see in regular schools) - but, this is not an excuse for giving up this demand to the Universities!!! Let's continue asking for what we need. Giving up is not an option.

[@mykofreder1682]

Assuming you understand calculus I used WolframAlpha for my PC, I have it because I knew it was a good math package and it was real cheap in Windows store, it relies on a backend server though and I crashed it entering a complex addition of several waves. Then enter the equations he blows over like (e^0.2it) or (e^2it) and see the results real and imaginary and the sin/cos breakdown. You can also enter the normal and normal square to see that |e^2it| or |e^2it|^2. His lecture would be helped if he had a math package on his PC and ran samples of the equations he wrote up there through a math package, shown on the overhead projector. The days of memorizing heavy or even light math are over, using the same math through a package long enough the memorization will occur eventually.

[@ankeunruh7364]

@@mykofreder1682 I do not believe something like 'understanding calculus', still trying to learn Lagrange formalism. I think, this is something to 'go through' - which means "shut up, follow, and calculate!". But: your advice "WolframAlpha" was a surprise, although it's not hidden (and never was)... In a school, we have to do more than I can oversee. Will try to get closer. Reflections welcome! :)

[@Andrewtmcb]

@@JaredBryan calc and linear algebrah strongly recommended

[@hasanshirazi9535]

When the Prof. rubs the chalk off the black board, doesn't it go into his open coffee bottle?

[@grandpaobvious]

Chalk is nontoxic when consumed in moderation.

[@hasanshirazi9535]

@@grandpaobvious Yes, may be Calcium in it is even beneficial for the bones!

[@shivam1996able]

if youre paying attention...the chalk is already in the coffee bottle, and also not in the coffee bottle

[@abderrahimbenmoussa4359]

There is.probably a function to assess that

[@jean-lucfacade6219]

Here I am. Looking forward to an hour long lecture on the Wave Function.

[@schmetterling4477]

Did you learn something?

[@KipIngram]

I 100% approve of the emphasis on dimensional analysis.

[@charliecooper7458]

IVE SEEN YOUR COMMENTS ON QUORA, You’re awesome!!

[@KipIngram]

@@charliecooper7458 Oh hey man, thank you. Let me make clear I am not a physicist. I'm actually an electrical engineer by training, and ever since graduate school 35 years ago I've just been really interested in physics and truly enjoy trying to help other people understand it. Alongside that, I have a few positions that aren't what you'd call "mainstream" (most re: consciousness), but I try to point those out if I mention them on Quora. Thanks for the kind words - I hope you have a great weekend. Stay safe and well!

[@youtubehandlesareridiculous]

What does his wife call his signature?

[@saqlainamin1951]

a wave function

[@AritraDaddy]

Are you sure? I think he started something on the lines of My wife calls it a little gift ... ?

[@liuculiu8366]

this question seems like some quiz appears in the English test, the listening part. And I forgot the answer when I see the question as I always did, lol!

[@Rockyzach88]

Yeah it's clearly edited out for some reason.

[@HighestRank]

Rubbish

[@AnuragPradhan101]

Why I'm feeling that this lecture is not in continuation with lecture 2 ,since in lecture 2 he didn't discuss polarization !

[@RedTriangle53]

he's referring to the group class held by the other professor, not the previous lecture. A group class is more like the classes you have at high school level and lower, in that you do problems and ask questions and sometimes they go through things on the blackboard. Edit: they might be using a different system than what I am used to, but I am at least fairly certain that he was talking about something similar.

[@financewithsom485]

Anurag Pradhan from Miami

[@Rockyzach88]

Polarization was just an analogy of how the box discussion.

[@arrabalimaz622]

I understand here in sir here till the 2019 and I had seen there 1 million subscription now it's 2.5 approx I'm quite happy

[@Peace-ey5hn]

IMO, a "quantum vibrational wave/ripple" is set off at the point where the electron is fired. A quantum aerodynamics of sorts. The wave precedes the electron. It is this wave that is responsible for the distribution pattern as each electron, even though fired 1 at a time, is carried on it. It explains the "probability" of where each would land. When you try to measure the electron, it is not the "conscious" act of doing it that causes the electrons to behave as particles, but it's because you break the wave. Thus, as there is no wave for the electron to ride on, it will come through the slit as an independent particle.

[@manavnaik1607]

Everytime I think to myself 'wow there's no way he has anymore room to write anything,' he pulls out another fucking blackboard out of nowhere

[@prn718]

8.04.1 = Look at me, I'm watching an MIT quantum physics class and I *get this* 8.04.3 = *head exploding*

[@drzecelectric4302]

Just what I need right now. Thank you!!

[@lisandrovenosta3865]

Excellent lectures, thank you so much. The cameraman couldn't be worse :D

[@akshaychandrashekaran4078]

At 39:02 Man, I was so excited to see that the postulate that covers everything about quantum mechanics was "FREE PIZZA". One cannot begin to imagine the disappointment that that was not the case :'(