Lecture 4: Expectations, Momentum, and Uncertainty

MIT 8.04 Quantum Physics I, Spring 2013
View the complete course: ocw.mit.edu/8-04S13
Instructor: Allan Adams
In this lecture, Prof. Adams begins with a round of multiple choice questions. He then moves on to introduce the concept of expectation values and motivate the fact that momentum is given by a differential operator with Noether's theorem.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@jasminecruickshank2343]

Let’s take a moment to thank whoever wrote these incredibly accurate subtitles

[@M_Lopez_3D_Artist]

Your welcome i did them

[@Therrhd]

@@M_Lopez_3D_Artistyou’re very appreciated

[@jasondean88888]

​​@@TherrhdSomeone who joined KZbin 3 years ago, did CC for a 9 year old quantum physics video, while incorrectly using 3rd grade English for "your"? And...that person actually found and responded to a comment (two and a half years after it was left) that was directed at them in the 4th episode of a 2 dozen long series? Not buying it.

[@edwardmadden1231]

Thanks 🎉❤

[@GuruCodeWriter]

@@jasondean88888 As you failed to use parallelism in your response (which is a 5th grade concept) and seemed to have forgotten the third item of your list (since you mention "joined" and "did" but forgot a third verb), I'm sure you have no reason to be commenting on this grammar issue, which does not interfere with comprehension, and you especially do not need to point out their late comment for two major reasons. The first reason is it should not matter, or KZbin would have removed the feature to remove a comment after a year, but no one cares and asks this to be implemented, which implies you shouldn't care either. The second reason is straightforward: you replied to this comment even later than the original reply which you are targeting. All this compiles into one question: why bother to a ridiculous response when you would make your claim even more questionable and grammatically incorrect? The difference between "your and you're" is simply an apostrophe, a mistake easily made by fast typing or a keyboard error, whilst your mistakes are conceptual and grammatical. Whilst it is likely that the user in question did not compile the subtitles, your reasoning is incorrect, for your evidence is simply correlations to why he couldn't have made the subtitles, not evidence of fact or experiment. Therefore, I'm not buying your argument and reasoning. (^ Hm, AI did a good job at this... or was it AI?)

[@SoulSnatcherSeven]

I’m so glad this series was created before he quit teaching this class. Wouldn’t want any other Parasocial Professor.

[@joaquinledesma1373]

''Whatever state you are in, we will always love you'' Can not fit more perfectly

[@TheBobathon]

Causal processes in QM lectures: we see the unintentional summoning of pirates at 1:07:50 ; they materialise four minutes later: 1:12:00 :)

[@dunuth]

7 years later: still the most underrated comment in the history of comments...

[@codenamerishi]

😂😂😂

[@accident_prone]

This Professor is awesome! Good lecture series. Thanks MIT for offering this quality content for free!!!

[@erikayer2146]

No kidding! Love this dude and am binge-watching these lectures. I'll probably watch his earlier lectures if they're available.

[@mkmalikcom]

@@erikayer2146 💯

[@maneki9neko]

He is terrific.

[@1349Sion]

Epic professor

[@brainstormedperson132]

The title if this video sounds like a description of my last relationship.

[@JA-it4bg]

Did anyone else almost cry at his enthusiasm when declaring that (hbar/i)d/dx is momentum?

[@KipIngram]

I would like to have had more discussion. I'd like for him to have gone through the details with Noether's theorem so that I could "feel it in my gut."

[@teddychoi8265]

19:39 Love the moment when you get to see all the little physicist in the making practice their hand waving arguments

[@ajitharidas9496]

Thank you, MIT for making such lectures available free for everyone.

[@timothyholloway5981]

Solid...gold! I wish I was in that lecture theatre.

[@StainedShuriken333]

I would love to have Allan as my instructor. He's so excited about physics and he's friendly. I've seen some talks that he has done as well, like with TED, and he's such an engaging speaker.

Oh thanks, i Will look his ted talks

[@northhamptonshire]

Allan Adams... You're my favorite teacher!!!!!

[@HT-rq5pi]

The lecturers at MIT really are amazing.

[@dutchboss509]

i like watching and would love taking his classes.. i find his lectures easy to understand and i like how he does not write cursive script on the board. very cool how hes always giving his audience positive reinforcement when they ask questions.. that and his happy demeanor makes learning much easier

[@KH-kp6gm]

56:03 I remember when I was first learning QM 10 yrs ago, I used to complain that the way of "deriving" operator p was definitely bullshit. Now this lecture gives me the salvation of my soul. Thank you, Pf. Adams.

[@ankitahalder9158]

Just loving this course especially because of Adams's way of teaching. I also liked clicker session and gave all correct answers. It's my request to ocw community, if possible please give the recitation videos as well. It helps in solving problems and assignments. Thanks for the great work MIT. you are helping lots of interested students.

[@Jop_pop]

This is literally the most clear and perfect teaching I have ever seen

[@EnchantedGardenGnome]

I just want to say I've never loved a teacher as much as professor Adams. He's SO good!!! His enthusiasm makes all the difference. Thanks for teaching!!

[@enisten]

1:07:55 Prof makes a Freudian slip - harbinger of later events - then laughs to himself 1:12:05 Clever bail out of the pranksters who make their appearance a bit too early 1:16:08 An allusion to the pirates appearing a few minutes ago or a foreshadowing of the next one? 1:17:00 Pirates invade classroom (again)!

[@enisten]

Ella Blun I'm testing people's will power and mental agility: Don't read past the point you see it coming.

The professor's energy its so awesome i definitely will finish all the quantum Mechanics lectures, its great to see someone teaching with this passion

[@craigfowler7098]

Fantastically interesting. He brings it alive with his knowledge, enthusiasm and sense of humour. Top draw dude

[@josemanuelgomez2501]

Big thanks to Allan Adams and all the teams that make this possible. Besides the business sense of giving out university lectures for free, the fact is that it is contributing to the spread of scientific knowledge, to anybody interested, giving opportunities to talented people regardless of country, level of income... And that's something that speaks high of the MIT, its mission and its people.

[@tejasbondre8229]

That ending was totally unexpected.

[@shijiechai9780]

Thank you very much Professor Allan Adams!

[@igorvasylchenko8293]

Thank you very much! Just have started watching lectures but they help a lot.

[@zeratulofaiur2589]

It is MUCH easier to understand Quantum Mechanics than those who spoke last couple minutes lol

[@spectralanalysis]

First person was saying that people who would describe lovely dames or beautiful people in the ancient past perhaps prophesied (suggesting 100% probability) the professor's existence, but praise is still not commensurate with his "worth to sing." Second person was saying that the professor's memory as a universally lovable person will always survive in the memories of posterity somehow despite monuments or statues of him being destroyed by war or washed away by tides

[@wafikiri_]

@@spectralanalysis Thank you for your summary. I only slept three hours last night, and was much confused by the verses, thus could extract no sense from them (although I've written [bad] olde poetry sometimes....). Whereas I could follow this professor's explanations very easily from start to end, English not being my first language notwithstanding. I agree with @Zeratul Of Aiur . . . 100%.

[@morgue1130]

urus you ur full time baby girl 👧 I miss ur too sweet uruturuturut uruserirrrriuruiiirrittiiiirriuitiittT I and urut are doing us using for some advice but usually I’m urusurut do get it urutmaybe but uruturut erirrrriuruiiirrittiiiirriuitiittT

[@tadebabatunde1999]

Its beautyful and interactive. calmly and professionally delivered lectuer. Thanks.Ade.

[@debnathsamanta2093]

His teaching skill😍..Thank You prof. and MIT

[@vaishalibanerjee7343]

The ending was just awesome...

[@anugrahmathewprasad172]

That quantum mechanics joke at the end by the pirates was gold..

[@dsfgoppudfgihdsf]

Ive watch this multiple times and it gets me every time.

[@alexmckinney9657]

I like how they applaud at the end of each lecture so far.

[@NoActuallyGo-KCUF-Yourself]

Probability of Shakespeare always = 1.

[@stumbling]

"To be or not to be, that is the probability distribution..."

[@skilz8098]

But what would be the probability of Chaucer?

[@user-ie2ur4ry5t]

His teaching skill..Thank You prof. and MIT. This class is masterpiece thanks professor, thanks MIT.

[@eliezeralvesmartins]

This class is masterpiece thanks professor, thanks MIT

[@SarthakGupta259]

1:19:27 Pirate guy: "whatever STATE you're in.." Prof Allan Adams: * laughs hysterically * Love the way of teaching, and the way he is in general

[@polevaultkid23]

This is amazing. Such a good lecture!

[@michaelborek378]

Explain this so well!! Thanks for these courses!

[@philippe2121]

Very nice & well explained ! Thanks for the awesome content MIT

[@MusicPlanety]

Que aula excepcional!!!!!

[@drrbpatel1265]

Extraordinary lectures, Awesome

[@NicolasSchmidMusic]

why aren't all professors at university so passionnate and motivated like this guy?

[@beenaplumber8379]

The physics faculty at the University of Minnesota had weekly meetings in the 1990's to develop novel methods of obfuscating the bloody obvious in undergrad courses. Allan Adams is my proof. He's actually got me convinced that my understanding is correct... most of the time. When I was an undergrad, my professors had me convinced I was wrong about the simplest things because I already understood the concepts without having to go through tortuous and bizarre logic to get there, and maybe because I understood that the quantum stuff, as it was understood then, was a lot of competing, mutually incompatible guesses, and nothing had really changed since high school physics a decade earlier. Nothing they'd teach at the undergrad level anyway. Nobody dared ask questions because the simplest question would result in a 15-minute droning, incomprehensible proof of the answer in detail that far exceeded the course content. And it wasn't just one guy. It was all of them that taught my classes. I quit coming to class except to take exams and my scores went up. That's like... anti-teaching. Professor Adams makes it so obvious how unnecessary and counter-productive that is. I might have enjoyed physics if I'd had professors who were a little more human.

[@schmetterling4477]

I think your professors had it right, after all. :-)

[@sam5992]

I still feel like he does it to a certain extent. The first lecture in the series was the worst of it, and he'd shush people asking questions immediately after saying that it was okay to interrupt him.

[@MrTiti]

you speak out of my heart. i had precarious family situations. got a heavy disease. went to hospital. failed. got even sicker. got more fatalities around me. didnt make it. and in the end yet my prof said my approaches are genius, but i was destroyed everywhere. the talent was destroyed, and so we all had no gains from this ... and so we have destryoed

[@wattsmichaele]

Don’t hurt on the Gophers!🥷

[@joseantoniogarciamerino1225]

Excelent Teacher. I will see all the course

[@demetrio6159]

Nice class, I love quantum physics.

[@LydellAaron]

Wavefunction is one definition of the particle's state, because there can be more than one wavefunction. You can sum wavefunctions together in a superposition. It may help to think of x as a "state" (NOT x as "position"). Then, momentum would then be the change of "state" or the evolution of the "state"

[@sepidehmajd593]

God bless you free MIT, YOU helped me a lot

[@clairezhao7869]

"Whatever state you're in, we will always love you." hahahaha! Excellent

[@yamenarhim9336]

Loved it too , I agree

[@tuha3524]

MIT is bringing freedom to a lot of students in the world.

[@tarunpachori8029]

thank you prof. adams

[@Liam2020]

Beautiful lecture, I love to watch these classes by Dr Adams, but watch out for the statement at 1:11:42 , that is a tricky road. To quote Einstein: "it's the theory that tells you what can you see". Dr Adams warns minutes before about this by telling that what he is going to say is an epistemic mistake, theories are not derived from data analysis but from a logical, profound and reasonable explanation of why and how things work the way they do.

[@abbiravindhran8424]

But doesn't the logical reasonable explanation somehow come from practice done before. LoL, you need to know that you are going to see before you know what something is going to tell you what you can see.

[@vianaautocenter258]

Thanks for the lecture I really appreciate it

[@Louis412e]

To anyone wondering how the evolution of viewers on the course acts (plotted): i60.tinypic.com/2cz6920.png I post this in the 4th video course because here is where the real decline happens.

[@Louis412e]

+Jovana Savic I haven't yet I feel like any phenomenon related to human determination will naturally be described by such a "curve".

[@Louis412e]

+Ella Blun Valid point. Quantum mechanics formalities can get quite confusing for an autodidact, so this decline is coupled to a huge progression in the complexity of concepts. I don't think anyone wants to work a few hours (2-8) at home on concepts he learned and would rather just watch the next lecture, yet it is necessary, in my opinion, to do so.

[@parthmaske3294]

At first it seems that it would take 24x1.3 = 31 hours to understand QM. But then come the lecture notes and mathematical concepts that pull you down. The transition in the course is not simple either. It goes like this: Lec1,2,2,1,3,3,4,4,5,5,4,1,3,5,6... How can we expect the viewers to be motivated and complete the course? Nonetheless, the series is an excellent resource.

[@arttuulmanen2399]

The evolution of viewers is not the same as the plot of the number of views per lecture though they are clearly correlated.

[@mattsmith9037]

Perfect boltzmann disribution,which is a basic rule of the whole universe.

[@charliehess9308]

“I’m going to skip the examples in the interest of time” always hurts to hear

[@andrewhudson3723]

Epic class, epic professor

[@blackhole1617]

Thank you sir Alan Adams

[@amuslim4225]

Amazing lecture :)

[@meetghelani5222]

I love this guy.

[@gamesbok]

Why are pirates called pirates? Because they Arrrrh.

[@anindyakantidey2794]

lovely lecture

[@jewgenijmoldawski3306]

Very cool professor!

[@davidchan4177]

19:32 nice convincing skills u have there

[@ahmedkamiss7643]

I felt like a student sitting in one of those benches. Thank you !

[@benny4013]

That was awesome!

[@homayounabtahi5832]

Now we can understand. Brilliant teachers +smart students = MIT = Nobel prize winning

[@ahmedgaafar5369]

quite awesome fantastic indeed.

[@Darthvanger]

Now it's getting weird :) I totally love how he introduced this, outlining that it's indeed weird, but also giving intuitions. When other teachers just write the formulas it's just overwhelmingly confusing and you're lost 100%.

[@blackhole1617]

Right man ... The way he related momentum with del x is satisfying... Great teacher

[@kyz]

i fell asleep and woke up to this, not disappointed

[@laitailai]

Very good lecture.

[@eyedeekay105]

1:10:42 - 1:12:05 wow that was awesomely passionate

[@valen8560]

yeah maybe that's the reason we like him, "physics doesn't tell you what is true... physics tells you it is a good model and it does really well and it fits the data. And to the degree that it doesn't fit the data, it's wrong!" this is really the heart of physics. we've never been told the truth by god, we've just been observing and proposing and correcting

[@BongboBongbong]

Multivalued function (vectorfunction) is (can be) a function of the form f(x)= x, y, z. It gives back multiple values, on different axis.

[@sebastiangillich6554]

If i can't be at the MIT, youtube bring the MIT to me...;-)

[@kettle351]

[@debasishraychawdhuri]

almost, not completely though. you cannot take a question to his office.

[@stumbling]

"you cannot take a question to his office..." [CHALLENGE ACCEPTED]

[@yamenarhim9336]

@@stumbling any update on the challenge i am interested

[@notintheobservableuniverse2594]

@Debasish Ray Chawdhuri some who are Introverts don’t typically ask something.

[@stormos25one]

The Show at the end... was truly unexpected!

[@swizzbeats1212]

Haha perfect ending for a perfect lecture!

[@Nehmo]

I didn't get it. Was it just a compliment? The lines weren't clear in meaning. 1:17:00

[@swaggerchegger98]

The probability distribuition of a continuous variable a is ALWAYS P(a)=0. In case of continuity the probability is solely described by a probability density.

[@swaggerchegger98]

which he actually says at around 45 min. Oops.

[@khajiit92]

37:00 i think what he's calling stad dev is actually the variance, and std dev is the square root of the variance?

[@DrzStudio]

From wiki page of variance: variance is the expectation of the squared deviation of a random variable from its mean...The variance is the square of the standard deviation, the second central moment of a distribution, so yes, the teacher used the wrong terms.

[@voltairesarmy6702]

I was thinking this too. But I wasn't 100% sure bc the notation is different than I'm used to.

[@TheMihaitza]

The coefficient of the integral describing δ(x-x₀) is 1/2π, not 1/√2π

[@snpkat465]

Around 22:20... I'd explain that it uses a large range of frequencies because it's a RECT function multiplied by the sinewave in time domain, which means a sinc function convolved with a delta function in the frequency domain. So you get an infinite number of decreasing sidelobes as you get further from the spike But then I come from a EE signal processing background, so I look at things a little differently

[@lery3510]

D Vill 👏👍Right the way EE thinking

Brilliant! sad that there are so little views

[@michaelallen5264]

I agree. They have half a million subscribers and less than 1k views on most videos. This series of videos is over most heads on KZbin though.

[@ArjitSeth]

Michael Allen Exactly. All they want to do is listen to Justin Bieber and watch "vloggers" instead of learning something.

[@Timer1012]

Haha, I am running into your comments more and more Mr Louw

Nice to see you have joined the party Mr Cassidy, unfortunately this means the enermies of hell grow stronger (diablo II).

[@Sergiosimpson1]

I agree with you, but usually people cannot find 1 hour to spend fully concentrated on this. These lectures are without a doubt awesome, but only for the ones who have the time and the energy to focus throughout 1 hour of complex science. Usually people in general tend to use youtube to relax and not to think, listening to music or wtaching vloggers, which can be relaxing.

[@kalecrosbie8878]

Description of Noether's Theorem was really interesting. I can't quite grasp how it must have a conserved quantity though, I might have to go through the paper.

[@lery3510]

Same here...(1st time hearing about Neother's theorem)

[@vijaybhushan1638]

I have a different way of saying the same thing. Look suppose we have a particle at position x=0 and we want to translate it to x=l. Now if the system has no interaction and an inherent definite momentum in positive x direction. We simply sit back and take our next observation at the moment it reaches x=l. We can claim that we have translated the particle without changing it's momentum state. Now suppose our particle has zero momentum at x=0, or we are not patient enough to let it reach x=l on its own then we cannot translate it to x=l without accelerating it. Then we will have to bring it back to its original momentum state after it reaches x=l. We can either accelerate and decelerate it to x=l. Or accelerate it and subject it to a collision so that it's momentum is restored to it's x=0 state. So claiming particle symmetry at two different positions requires the particle to be at same momentum state in both the positions. Remember Sir explained that to fully define the state of a particle in classical sense we need to know it's position and momentum. Hence we see translational symmetry dictates momentum conservation. Now you should consider the case if we perform same experiment at different places with identical but different particles. What's the condition for translational symmetry for this case?

[@theonebucketlist]

This Professor is so much better than mine! Are all professors in the US this cool? should have applied to MIT!

[@mpodevin]

In the second clicker question, which asks "which particle has larger momentum?", it is not specified that each particle is an identical particle; therefore, isn't D the correct answer given that particle 1 and particle 2 could have different masses? I guess you could make a semantic argument about the definition of "wave form", but even then they could have the same wave form and different masses.

[@ravenecho2410]

just quick heads up when he says standard deviation he means variance, standard deviation is on order (1), and is the square root

[@jesalkotak5595]

5:55- shouldn't it be superposition of the wave function down and up? which results in the wave func.=upper one

[@palashpal2926]

Very very thanks

[@debasishraychawdhuri]

Do a superposition of talking to the person left to you and talking to the person right of you.

[@SandyDD17]

Amazing

[@KipIngram]

1:10:45 - I'd really like to see more about that relationship. Just "declaring" it is terribly unsatisfying.

[@iamcheck.thisout]

happy valentine's day!! @ MIT

[@zokalyx]

can the wave function depend on time as well? for example the localized spot moving as a funciton of time to represent a particle moving

[@flikkie72]

I just realized for the first time these lectures are 80 mins, here I was thinking that these 'hours' went by faster than in my uni 😅

[@xandersafrunek2151]

that's a very good question

[@maythira87]

Other girls: being big fans of actors, singers. Me: being a big fan of a physics professor He is so awesome. These students are so lucky to have him as a teacher.

[@wulphstein]

Could wave functions be describing virtual photons, the ontological counterpart?

[@imransaeed3024]

EXCELLENT VIDEOS AND WAY OF DELIVERING . Where can i find problem sets

[@mitocw]

Problems sets with solutions can be found in the Assignments section of the OCW course website: ocw.mit.edu/8-04S13.

[@Ztingjammer]

@@mitocw send some love from Sweden to Allan Adams. He's amazing!

[@blackhole1617]

Tough but fun class today 😌

[@Swanke]

Do the rules of probability density apply at the event horizon of a black hole with regards to Hawking radiation and virtual decay?

[@Krish_202]

No it doesn't, as we never know the presence of virtual particles but for expecting a quantum fluctuation around the event horizon so expecting the norm square of psi(x) would be really bad P(x) ≠ | psi(x) |²

[@Nehmo]

1:17:39 The watch is incongruous with the outfit and language.

[@denhol8247]

Education is about content over form. Bigotry is about form over content. Guess what? This is education.

[@subject319]

Calm down MLK, I'm sure there are other, slightly more important battles to pick than calling someone a bigot for a throwaway observation about a watch.

[@denhol8247]

Indeed, just as I am sure that you must also have far more important battles to pick than to comment on such an trivial observation my friend.

[@physicsdemonstrations2426]

English not being my first language, I didn't understand anything from the last part, would love to know though, they sure sounded full of praise for the professor.

[@hamidrezaakhlaghi2348]

the age example can be found in the Griffith quantum mechanics