Advanced Quantum Mechanics Lecture 1

(September 23, 2013) After a brief review of the prior Quantum Mechanics course, Leonard Susskind introduces the concept of symmetry, and present a specific example of translational symmetry.
Originally presented by the Stanford Continuing Studies Program.
Stanford University:
www.stanford.edu/
Continuing Studies Program:
csp.stanford.edu/
Stanford University Channel on KZbin:
/ stanford

[@joelcurtis7447]

The first hour of this lecture might be the best higher-level crash course in QM to be found. Very well presented.

[@waynelast1685]

I have to disagree. It has some useful ideas but there is a lot missing. It is just a quick lead in to subsequent material. He is getting people used to working with operators.

[@princeistalri7944]

This man is an incredible teacher, he makes even the most abstract concepts approachable and understandable.

[@noditschi]

He makes them sound trivial, like eating a pizza slice by slice!

[@RexGalilae]

Prince Istalri One of the greatest friends and admirers of Feynman has to be this smart and great at explaining don't you say? ;-)

[@shellydas1416]

Agreed

[@ciscobriones5904]

I agree, even the Avg American with a working brain can understand it!

[@SimonEarly]

I cant believe this material is so freely available and good. Just like being back on my course 25years ago but this time I can pause the vid to try and get my head round it all (again!). Students today dont know how good they got it :-)

[@fermibubbles9375]

We know my friend, we know

[@eric_welch]

There is no doubt about how good we have it ...i thank the "giants" upon whose shoulders i stand daily :)

[@eric_welch]

neil u because it’s the anti electron which by the conservation of momentum and lepton number is required to be opposite in charge ...we also know that when a positron and electron interact they annihilate one another and produce a photon of light which only happens with particles of equal but opposite charge

[@eric_welch]

neil u check out the first chapter of Griffith’s intro to particle physics ...it is approachable even for the novice to particle physics

[@eric_welch]

neil u spin is also involved ...fermions have half integer spin ...by the Pauli exclusion principle the two fermions cannot exist in the same quantum state or in other words have the same quantum numbers simultaneously ...field theory uses second quantization to handle this through creation annihilation operators and slater determinants to ensure anti symmetry

[@franklinenfor9592]

One of the best Physics prof. He breaks down complex things and makes them so easy to understand.

[@garywpearson1955]

Lenny, you are the kind of wonderful genius that makes such a difficult topic so accessible. Your natural warmth makes one absolutely ENJOY your lectures. Can't do better than that! There ought to be a "Professor Lenny Susskind" commemorative stamp. One of my very favorite American heroes!

[@arunenquiry]

What I love about Prof. Susskind is that he not only shows us the Mathematics, but also tells us the meaning of the Mathematics. That kind of understanding is difficult to get from texts.

[@franklinenfor9592]

True

[@miarencrowsdaughter6434]

Just in time for the holidays! Dr. Susskind, if you read these comments, I have greatly enjoyed all of your lectures.

[@lalaloxx44]

Awesome vid!! Thank you to this professor.. he does an EXCELLENT job of teaching new concepts!! I’m a hobbyist, and enjoy watching these in my spare time to learn more about the world and how it works. Very informative and much appreciated.☺️👍🏾

[@kuonirat]

Can't believe a lecture on advanced quantum mechanics has over 100 000 views... Not a dancing kitten level, but still there is hope for humanity.

[@TheSiddharthCool]

You see, there are many Indian and Chinese..so...

[@inspiration1883]

Not Interested haha, I'm Arabian.

[@prolekzkurios]

there is hope. but in the year 3000.

[@prolekzkurios]

you can undestand even economy with quantum mechanics!!! since is related with maths and stadistics and many more.. time travel, bilocation, nature..

[@tirthachakrabarti5912]

Don't forget Computing and communication. Computing is everywhere. To tell nothing about communication. QM is gonna give us Quantum computer and Quantum communication.

[@davidludwig3975]

I love this stuff being available to everyone. KZbin is the modern university.

[@JefferyCarrNYC]

It took me until minute 15 to decide "ok. This is going to be really interesting". Thank you Susskind & Stanford for putting these on youtube. I hope I can grok it.

[@terryschmidt3413]

wow, thanks! I just don't get enough of quantum mechanics during the day. :o)

[@JimboMack]

I can't believe we have the likes of Leonard Susskind's to teach us so freely, i think it is amazing that these Goliath's of science aren't much more appreciated.

[@caner78bob]

i lost him when he put the marker on the board

[@usaviation2281]

i lost him when he said his first word

[@ciscobriones5904]

@@usaviation2281 I can keep up with what he is saying, does hurt the brain a little but in a good way.

[@yeshacroe9354]

bruh me too

[@frede1905]

Absolutely phenomenal lecture. Very clear and concise.

[@alijavan3831]

Quantum physics is something abstract at least in our daily routine life that always needs to be imagined. Here Prof. Leonard Susskind visualizes so many simple known mechanical facts in quantum, therefore, everyone even those with a little level of physics understands them very strongly.

[@schmetterling4477]

So you didn't understand the first thing. Well, he didn't explain it well. ;-)

[@EnthusiasticCoder]

Excellent he's back!

[@milanpaudel9624]

oh my lord, I cant watch this right now, since My final exam in Account is within a month, But this is so tempting. I have been doing lots of self study, never in my dreams expected this is to be so freely available. . I just hope this doesnt get removed any time soon.

[@kwgm8578]

Lenny is a down-to-earth version of Dick Feynman, who could be too brilliant for everyone else in the room. He's an excellent teacher who never resorts to hand waving, but follows through with clarity on every detail. If you are one of his students, and are willing to do the work, I would expect that he would make sure that you succeed.

[@praiseafrogtoday9114]

Wow. I just graduated 5th grade and wanted to expand my knowledge on quantum mechanics to prepare for middle school. I think that this video was a great lesson and I look forward to watching the rest of this series.

[@justlivin3998]

Bruh

[@qbtc]

At a minimum, you should watch his Classical Mechanics lectures followed by his Theoretical Minimum (quantum mechanics) lectures before this one to get the most out of it. You should be familiar with the product rule and chain rule of differentiation, integration by parts, basic matrix algebra like dot products and determinants. Familiarity with Fourier series and transforms helps a lot also.

[@azmard4865]

this content is so superb that I want to put it on my cv 🤣❤️

[@lupi2000]

Very interesting! I love prof. Susskind, especially when he eats his cookies! I've been attending all his lectures, It'll take years... :-) thank You prof!

[@hasanshirazi9535]

Great revision of the QM1 course. @1:19:33 For the first time QM matches common sense: Q: "What requires V to be unitary?" A: "It is an assumption that symmetries of nature take orthogonal states to orthogonal states... that seems plausible..."

[@Milkra]

Just finished binge watching Rick and Morty, this all makes sense to me now

[@aghaadnan5771]

I didn't believe these complex concepts can be explained so simply..... I was stranded in the deep woods of QM but Susskind's lectures are a source of light......... here I practically see einstein's words 'only he who understands can make others understand' ... btw these are the inverse of Einstein's actual words...

[@user-pz7ys3mf8u]

I read about orthogonality But no one explained it as this professor did He is just incredible

[@htfx11]

59:15 The definition of the time independent Sch.Eq. that is the eigenvalue equation, beautiful

[@DavidGoodmanLondon]

75 this year? going strong :) keep up with good material.

[@roycorpuz5054]

just came here to get mind blown...MIND BLOWN!!!

[@JoyTheDataScientist]

If you want to follow along with Sakurai's Chapter 4, start at 1:20:00 ish.

[@joeNonos]

fabulous, here is just a basic lesson about the quantum mecanic but we can see already a implied reference to the "pullback" property (category theory) and a allusion to the "Noether" theory

[@htfx11]

56:20 Beautiful derivation of the Sch. Equation

[@quantaali543]

1) Review 00:13 2) Unitary time evolution and generator of time evolution 29:38 3) Translational symmetry and its generator 1:02:36 Next: Generator of Rotation and its generator.

[@ginnyarmstrong9456]

I am 13 and I love this stuff. Don't say it is boring, because it is not. Quantum mechanics opens up all kinds of possibilities. Quantum computing for example is just one of the many uses of quantum mechanics. The amount of possibilities is almost as mind bogeling as the psysics itself.

[@amjidali588]

Ginny Armstrong 🤓

[@antrikshrathore5151]

You are 13 already? Dang, Im only 3 years old and yes all those equations are so interesting. I love quantum mechanics. I already have 5 published papers in quantum physics. Excited to see what the future holds

[@rangolisaxena90]

Would it be possible to get the lecture notes of these lectures?

[@dottywhl5335]

I watch these to fall asleep but it’s too interesting and I stay awake 😮😮😮😮

[@richos07]

Remember it’s not about whether you can read sheet music, it’s can you hear it. Can you hear the music Robert?

[@ThomasSchuuring]

The only bright thing in 2017 that's not something god forbid, is being able to study advanced quantum mechanics from freaking youtube. I'm now half an hour into the lecture and i did watch a thousand documentairies on this, but i still had to go trough almost 20 wikipedia pages to nearly understand half of what he's saying. I'm not stupid but i didn't realize that even considering an actual thought about this subject requires a lot of skill. Skill i've got to catch up to. But it's still realy amazing to find this kind of knowledge out here.

[@DApple-sq1om]

Nobody does it better than Leonard "Leonardo" Susskind, makes me feel sad for all the rest. Why'd you have to be so good.

[@erwinmarschall2465]

1:15 It's easier to remember as a "commutative diagram" (as mathematicians say): |s1> -- U --> |s2> | | V V | | v v |s1p> -- U ---> |s2p> or UV = VU

[@Zeppy8yppeZ]

you mean 1:15:00 ?

[@bobbicals]

That's exactly what he drew

[@SalvatoreIndelicato]

dear professor can you please enter the English subtitles in his last lessons on the internet. Thank you

[@GreatVomitto]

This is going to be good.

[@2min.philosophy358]

how to visualize a wave function ? it will be helpful in contribute to the development in QM

[@gnickthegnome1981]

Im gonna be honest, I leave this on in the background because I can't possibly comprehend what he is saying and it is helping me get work done. LMAO

[@fofagery92]

yes, i will be busy all tonight!!

[@axvle]

Christmas came early this year! :)

[@gavrielcana]

who would put a thumbs down? i dont understand jack but i love this..why a thumbs down? someone who loves biology?

[@black_jack_meghav]

Lol I'm also curious bout this

[@hadifromlebanon3812]

can we get the lecture notes or they aren't available?

[@fjficm]

Most of these students asking dumb questions should revise prior to doing Advanced QM. Both Heisenberg matrices and Schrodinger pictures are required in QM as the first describes the discrete quantifiable eigenvalues of the eigenfunction psi whereas the Schrodinger picture describes the continuous picture of a quantum picture. Schrodinger picture is always the initial state of a particle. The Heisenberg picture better describes measured states like angular momentum, spin etc ie values of observables

[@cryptonitor9855]

Hm.. Asked a question on a previous lecture a few minutes ago. I think this answered it. Re-watching this to prepare for the coming thesis ;) I recommend everyone do the same. Brush up on your understanding of "how read this and see where it should envelope". Might be released tomorrow if tonight is right lol ^^ Check sci-journals. Thanks LS

[@RexGalilae]

This is the part of KZbin where we sift out the real fans of Physics and those kids who pretend to know physics after having watched Interstellar

[@ultradude2491]

Rex Galilae interstellar has manny flaws - some are only in sci-fi.

[@Zeppy8yppeZ]

No, you should specify "Marvel Kids".

[@unpredictablegenius8463]

How do u know they're faking it?

[@unpredictablegenius8463]

I'm only 14 and studying this stuff

[@ladenbinosama2776]

Lmao, I had a kid like this in middle school, he would use fancy words that he didn't know the meaning of after watching a simple physics video and when asked what they mean he would just say "oh you wouldn't understand".

[@bleu2663]

I’m listening to this tonight because I have insomnia and want to fall asleep

[@petergreen5337]

❤Thank you very much Professor and class

[@nomadsland7195]

Where is the full couese available online?Can anyone plz tell?

[@Waranle]

Where can i find the lecture notes, thanks

[@noni6513]

I dont know

[@kigvader]

@1:35:04 how is shifting to the right not + epsilon? but - epsilon instead?

[@GeneralPet]

25:20 He said that Ψ(x) = , but in the momentum eigenvalue equation he simply replaces |Ψ> with Ψ(x). Why?

[@pinklady7184]

This professor's name is Leonard Susskind. I will check him out in KZbin.

[@Lou-jf4rl]

Is there a better introduction to this class?

[@lonestar2779]

I love this guy... AMAZING.

[@RCrosbyLyles]

Curious about the choice of words orthogonal versus linearly independent?

[@schmetterling4477]

Orthogonal means the scalar product of the two vectors is zero. Linear independence means that no linear combination of the vectors is the zero vector.

[@seungsoolee1949]

Why can we just change the signs at 47:32? I get that we want the G^hermitian = -G to become H^hermitian = H, but wouldn't that affect the U(t)psi? thank you!

[@AndrewSanchez11235]

We add the imaginary number i because by definition U^dagger means to transpose the matrix and take the complex conjugate (also known as taking the Adjoint of the matrix). So if H is real, we can;t just change the sign of H by taking U^dagger; that is, if U = 1+eH and H is real, then U^dagger = 1 + eH. But if we add an "i" in front of H then when we take the complex conjugate we actually get the sign change we wanted, that is, if U = 1 + ieH and H is real then U^dagger = 1 - ieH. Of course, the Hamiltonian is complex because H = -ihp^2/2m + V(x) = -ih/2m (d^2/dx^2 ) + V(x) but -H does not equal the complex conjugate H* (to see this multiply H by -1, then actually take the complex conjugate H*. You'll see that -H does not equal H*).

[@SalvatoreIndelicato]

missing subtitles. You can insert them?

[@ghassanaber9368]

you found a subtitle ?

[@MeLoonn]

Yay ! More Susskind !

[@Devast8r34]

Thank yall

[@dulamel]

Just revisiting my 1st grade math class.....

[@riasatchowdhury5406]

I suddnely opened the video. Can anyone tell me is it langauge speaking class and which langauge he is writting on the board??

[@kidpog3d101]

i just typed in advanced ohysics and never did physics before and understood a lot. I wish german schools were like this

[@schmetterling4477]

German schools are like that. Some are even better. Susskind is not very good at teaching the basics.

[@GDubs13]

Excellent

[@AlonsoRules]

4:20 complex numbers are ubiquitous in quantum mechanics - so does that mean that the square root of a negative number is the only way to explain it

[@lsbrother]

Can someone explain why these lectures (and other videos) are posted many times on KZbin - by Stanford but also by lots of other people - when you view them they seem to be exactly the same ones. Why do lots of other people publish the same stuff? - what's the point?

[@0xpatrakar]

I think only stanford has posted lectures but too many people have created playlists

[@bhaaarat]

at 1:26:24... those(H & H dagger) are hamiltonians and not hermitian

[@tuber12321]

At 1:08:40 he says that the operation might correspond to squeezing or stretching, which are not symmetries. But then a few seconds later he requires that V be unitary. Did I miss something?

[@netrapture]

He uses V in the first case to say that doing anything corresponds to multiplying on the left by an operator. Next he is talking about operators representing symmetries, and he uses V again, a particular case of the first V. It's commonly done in mathematics, called AOL "abuse of language"

[@matstnilsson]

Awesome!

[@jpisar11]

does the time operator (U(t)) is a symmetry?

[@MrLethalShots]

If H does not explicitly depend on time then yes. This is because U(t) is constructed as a Taylor series in H. Therefore U(t) always commutes with H. The consequence of this is that energy is conserved in time. For a H that explicitly depends on time it is more subtle and I am not educated enough to give the answer. I know this is 8 years old but I thought it may help someone else.

[@davidwilkie9551]

"Someone" should make a comments list on Henri Bergson so-called Philosophy of Time, for example what,how and why is it not simply just another interpretation of the Arrow of Time and Relativity in the Correspondence Principle format. In the ONE-Infinity unity-connection categorization of e-Pi-i logarithmic resonance Partitioning of self-defining temporal phenomena, a musical-pure-math continuity to instrumental device idea.., the image of conic-cyclonic quantization cause-effect is an aspect of ONE-INFINITY Singularity Quantum-fields Mechanism Holographic Principle. Some math-musical thinking practice.

[@maccollo]

I DON'T UNDERSTAND ANYTHING! But it is interesting nonetheless.

[@jackhooper2839]

***** no, watch videos of simpler concepts, buy textbooks for those concepts, do the questions until you fully understand, then rewatch this video.

[@vincent8716]

It takes some time to unlearn concepts that you grew up with and are considered 'common sense'. If you watch the "MATH YOU NEED FOR QUANTUM MECHANICS" lectures first, at least the mathematical terminlogy becomes much clearer.

[@xOxAdnanxOx]

vincent can you tell what type of math is really needed in QM? calculus and differential equations aren’t enough for it?

[@tuber12321]

@@xOxAdnanxOx Differential equations are really only needed if you want to solve particular problems. Mostly (abstract) linear algebra.

[@phildurre9492]

The thing about QM that i dont like is that you never know H. And if your experiment is different than expected, you just try a different H, until it eventually explains the observations. Its like a theory with a parameter that you can guess, you may aswell just guess the results. At least thats my feeling at the present.

[@miguelgomezdonoso5671]

+phil durre All theories are like that. You have some equations, some constants, some rules, and you try different ones until theory matches. The crucial thing is that once it works, it works all the time within its range of applicability, which NEVER is just one particular instance of an experiment, which would be equivalent to "introducing the results by hand" or "guessing the results", as you described it.

[@niazikhan8754]

sir I need problem solution chap first of modern quantum mechanics by j.j sakurii edition first.can u help me in this??

[@Paul-im7pd]

how far does this professor walk every session?

[@silent_traveller7]

Hmm, Lets do poors man calculation. Videos are generally 2 hours long and assuming he stands for 1/4th the time to explain stuff and other 3/4th the time walking and writing on the board. So total time he walks is more like 1 hrs 30 min. Now assuming an average walk speed to be 1m/s. Calculating its in hour gives us 3.6km/hr. Now hence putting it in vt=distance we get, 1.5hrs*3.6km/hr=5.6kilometers each session. Hail lord fermi.

[@shingtome2179]

This is exciting

[@shrimpjar2]

Thanks for the help! Now I hope you will be able to guess where the electrons of my mouse will be, because not even Schrodinger's equation can guess that my mouse would be hovering over the subscribe button!

[@manou4118]

wonderful

[@farhanayan5335]

I want your help in M phil how can i contact you

[@jyotibaadal8335]

which book he is following?

[@oatsentertainment]

jyoti baadal yeah im not sure either lol. Are you phys major?

[@archanabasnet751]

Awesome!!!!

[@mamunurrashid5900]

In 44:48 , what requires this operator to be Hamiltonian? Shouldn't any Harmitian operator be just fine?

[@jasperbutcher2596]

I don't think he proves that here, but the hamiltonian corresponds to the energy of the system. It appears in the time-dependent schrodinger eq which in turn comes from the assumption that the evolution of the system is governed by some operator which is to be close to H for small time spans. Its just a matter of where you create it and where it is significant. idk if this is exactly what you asked. kzbin.info/www/bejne/qoO6c6KlqNh6Zrs could help too.

[@JB-lu7vz]

Every time I get full of myself and think I am knowlegable, I watch a video like this and realise I know nothing.

[@shellydas1416]

Its tough but it give it time ull get it!

[@hamzaikanna1507]

thank you

[@physicsguy877]

In the part where he talks about conservation of information, why does he insist on 2 states being observably different being the same as the 2 states being orthogonal? Aren't two states that aren't multiples of each other but with non-zero inner product still observably different? What am I missing? Thanks!

[@Delfigamer1]

He talks about it at length in his basic QM course. In short, when we perform a single measurement of an observable Q, we can only get one of its eigenvalues a, and then the state of the system collapses to its corresponding eigenvector |a>, meaning that the previous state is irreversibly lost. We say the states |a> and |b> are 'observably different' when threre exists an observable Q, such that after measuring Q we can say with certainty whether, before the measurement, the system was in state |a> or in state |b>. Due to math, this condition is equivalent to |a> and |b> being orthogonal - when they are, we can possibly craft an experiment to distinguish these two; when they are not, such an experiment cannot exist even in theory. A practical example is the spin of an electron. We can easily measure between electrons in an |↑> state and a |↓> state, but there is no possible way to reliably distinguish between electrons in an |↑> state and a |→> state, because they are not orthogonal, |→> = (|↑> + |↓>) / √2

[@RicardoHernandez-nd5pp]

Please, no translation, but reproduce down or above the screen the lecture. Thanks

[@rajeshwarchinna]

I just searched n opened it to get good sleep, thanks

[@amjidali588]

Can someone refer the vector to the operator?

[@Urdatorn]

Hardest part is the Leonard Equation, I still haven't solved it.

[@literaturewithjayneel]

sublime

[@josjimkes7275]

question: Do the symmetric transformations take up time?

[@AndrewSanchez11235]

Physically transformations take time. It takes time to, say, rotate and object. But mathematically we consider operations happening independent of time; that is, for a rotation of phi radians, R(phi) we only consider the change of the state with respect to the rotation; R(phi)|psi> = |psi(phi)> where |psi(phi)> represents the state |psi> rotated by phi radians. So, mathematically, we treat the rotation as happening instantaneously.

[@jpdiegidio]

No time. The point is you are rather translating/rotating/etc. your frame of reference.

[@yogeshkumarchaudhary5681]

At last why psi(x+€) is replaced by psi(x-€) ? Displacement was toward right side.

[@JoyTheDataScientist]

Graph out x^2 and compare it to (x-1)^2. Watch that it shifts to the right. So a right shift on f(x) is defined by f(x-a)

[@social3ngin33rin]

oh gawd .-. didn't know he taught an advanced version D:

[@george_is_a_greek]

Didn't understand this lecture, I have only completed A-level maths is this enough to understand this course?

[@seeme8080]

No

[@miguelaphan58]

...this is hard rock pysics, it hits hard in the brain...if you got one!....

[@mustafaercumen8436]

Can you add Turkish subtitles i Love Quantum mechanische But i cant understand english