Advanced Quantum Mechanics Lecture 1
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- čas přidán 5. 09. 2024
- (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 CZcams:
/ stanford
The first hour of this lecture might be the best higher-level crash course in QM to be found. Very well presented.
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.
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 :-)
We know my friend, we know
There is no doubt about how good we have it ...i thank the "giants" upon whose shoulders i stand daily :)
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
neil u check out the first chapter of Griffith’s intro to particle physics ...it is approachable even for the novice to particle physics
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
This man is an incredible teacher, he makes even the most abstract concepts approachable and understandable.
He makes them sound trivial, like eating a pizza slice by slice!
Prince Istalri
One of the greatest friends and admirers of Feynman has to be this smart and great at explaining don't you say? ;-)
Agreed
I agree, even the Avg American with a working brain can understand it!
One of the best Physics prof. He breaks down complex things and makes them so easy to understand.
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!
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.
You see, there are many Indian and Chinese..so...
Not Interested haha, I'm Arabian.
there is hope. but in the year 3000.
you can undestand even economy with quantum mechanics!!!
since is related with maths and stadistics and many more.. time travel, bilocation, nature..
Don't forget Computing and communication. Computing is everywhere. To tell nothing about communication. QM is gonna give us Quantum computer and Quantum communication.
Rehearsing QM formalism; Symmetry 1:02:45; Symmetry operator is Unitary 1:09:00; Symmetries commute with Time evolution and hence with Hamiltonian 1:16:30; Discrete and Continuous symmetries 1:23:30; Generating function is Hermitian and commute with Hamiltonian 1:25:30; Translation symmetry example to derive momentum operator 1:29:00
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.
True
i lost him when he put the marker on the board
i lost him when he said his first word
@@usaviation2281 I can keep up with what he is saying, does hurt the brain a little but in a good way.
bruh me too
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.
this content is so superb that I want to put it on my cv 🤣❤️
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.
So you didn't understand the first thing. Well, he didn't explain it well. ;-)
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.
This is the part of CZcams where we sift out the real fans of Physics and those kids who pretend to know physics after having watched Interstellar
Rex Galilae interstellar has manny flaws - some are only in sci-fi.
No, you should specify "Marvel Kids".
How do u know they're faking it?
I'm only 14 and studying this stuff
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".
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.
wow, thanks! I just don't get enough of quantum mechanics during the day. :o)
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.
Just in time for the holidays! Dr. Susskind, if you read these comments, I have greatly enjoyed all of your lectures.
I love this stuff being available to everyone. CZcams is the modern university.
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.
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.
Bruh
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.☺️👍🏾
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.
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.
Ginny Armstrong 🤓
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
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..."
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
Just finished binge watching Rick and Morty, this all makes sense to me now
If you want to follow along with Sakurai's Chapter 4, start at 1:20:00 ish.
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
you mean 1:15:00 ?
That's exactly what he drew
I read about orthogonality
But no one explained it as this professor did
He is just incredible
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...
I DON'T UNDERSTAND ANYTHING!
But it is interesting nonetheless.
***** no, watch videos of simpler concepts, buy textbooks for those concepts, do the questions until you fully understand, then rewatch this video.
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.
vincent
can you tell what type of math is really needed in QM? calculus and differential equations aren’t enough for it?
@@xOxAdnanxOx Differential equations are really only needed if you want to solve particular problems. Mostly (abstract) linear algebra.
59:15 The definition of the time independent Sch.Eq. that is the eigenvalue equation, beautiful
I watch these to fall asleep but it’s too interesting and I stay awake 😮😮😮😮
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
56:20 Beautiful derivation of the Sch. Equation
Remember it’s not about whether you can read sheet music, it’s can you hear it. Can you hear the music Robert?
I’m listening to this tonight because I have insomnia and want to fall asleep
who would put a thumbs down? i dont understand jack but i love this..why a thumbs down? someone who loves biology?
Lol I'm also curious bout this
how far does this professor walk every session?
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.
Excellent he's back!
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
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!
Absolutely phenomenal lecture. Very clear and concise.
just came here to get mind blown...MIND BLOWN!!!
75 this year? going strong :) keep up with good material.
Just revisiting my 1st grade math class.....
at 1:26:24... those(H & H dagger) are hamiltonians and not hermitian
Leonard Susskind is just like Dumbledore of Quantum physics )
"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.
Cant tell if my brain hurts or if im just smarter
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
Please, no translation, but reproduce down or above the screen the lecture. Thanks
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.
+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.
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.
yes, i will be busy all tonight!!
“No man in all Israel was as handsome and highly praised as Absalom. From the sole of his foot to the top of his head, he did not have a single flaw.”
2 Samuel 14:25 💕
I know His perfectly Proportion
He is God
Glossary of associated e-Pi circularity and i-condensation superposition identification of conventional-temporal phenomena.
(Preliminary "sufficiency" analogue to comprehend time-timing sync-duration identification)
Hermitian Operators are Real Number, Quantum Theoretical, temporal superposition real-time associations.
abstract Quantum numberness vector-values.
Eigenvalue Hermitian Operators-> (quality of floating frequency?) multiplies (amplitudes?). AM-FM Communication?
"Orthogonal", ? approximately "the illusion of separation", (phase-locked?) between quantization identification vector-values (Singularity positioning integration?)
Zero-infinity 1st law of thermodynamical orthogonality, because axial-tangential Geometry, 2nd law point-line-circle time-timing e-Pi sync-duration i-reflection phase positioning-location conic-cyclonic condensation, Eternity-now Interval Reciproction integration, in Singularity-Apature Perspective Principle.., is holistic holography, vector-values dimensionality. "Recording" or Imagery.
"Wave function times its Complex Conjugate is always positive", (intuitive convention provision), because multiple, superimposed vector-values, are real-time potential possibilities and probabilities, existence sync-duration, multi-dimensional connected, (observable-> n D dominate probability vector-values), Condensates mass-energy-momentum continuous creation cause-effect connection. Operational Principle of Calculus eg Chain Rule => Dimensionality coordination.
-----
Students should choose their own reiteration and reintegration patterning. "Yesterday is gone".., and never was..
Can someone explain why these lectures (and other videos) are posted many times on CZcams - 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?
I think only stanford has posted lectures but too many people have created playlists
Why do Stanford inactivate the comment-section on some videos?
probably because of your spelling and grammar.
Nuel2080 What's wrong?
nothing m8 :)
Gunnar Karlsson i agree whats the point? Do want controversy or? 🤔
Yay ! More Susskind !
i just typed in advanced ohysics and never did physics before and understood a lot. I wish german schools were like this
German schools are like that. Some are even better. Susskind is not very good at teaching the basics.
dear professor can you please enter the English subtitles in his last lessons on the internet. Thank you
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
Every time I get full of myself and think I am knowlegable, I watch a video like this and realise I know nothing.
Its tough but it give it time ull get it!
which book he is following?
jyoti baadal yeah im not sure either lol. Are you phys major?
Symmetries in nature:
When electrons fill up shells in atoms: 2, 8, 18, 32, 32, 18, 8 (seven shells), and given that energy in this universe could freely flow if nothing stopped it from doing so, then a natural bell shaped curve would suggest that an eighth energy shell could exist with a maximum of 2 elements in it. Chemical element #119 (8s1) and Chemical element #120 (8s2).
#119 I put at the bottom of the Hydrogen group on the Periodic Table of the Elements and #120 I put at the bottom of the Helium group on the Periodic Table of the Elements since it's outer shell is full of electrons. Their respective positions on the table would help dictate their properties.
#119 would have one electron in it's outer eighth energy shell with room for only one more electron. It's possible that energy could enter the atom through this opening and then most of that energy gets trapped inside of the eighth energy shell. Hence we would possibly perceive a black hole. I believe it might be possible to find element #119 inside the center of black holes.
#120 would have all 120 of it's electron spots filled. When a neutron split inside of this atom (giving off one proton, one electron, and energy), the proton, electron and energy would be ejected from the atom as they would have no place to go in that atom. One proton and one electron is basic Hydrogen (of which the Sun is primarily made up of) and the Sun certainly gives off energy. I believe it might be possible to find element #120 inside the center of stars.
Since we will probably never be able to enter inside the center of black holes or stars, look at black holes and stars as if this were true and see if we see what we would expect to see if this were really true. "If" true, or even somewhat true, it might just give us a better model of the universe to work with than we currently have. Plus, it would finish off the Periodic Table of the Elements. Check done, what's next?
❤Thank you very much Professor and class
sublime
Where can i find the lecture notes, thanks
I dont know
Nobody does it better than Leonard "Leonardo" Susskind, makes me feel sad for all the rest. Why'd you have to be so good.
how to visualize a wave function ?
it will be helpful in contribute to the development in QM
25:20 He said that Ψ(x) = , but in the momentum eigenvalue equation he simply replaces |Ψ> with Ψ(x). Why?
Christmas came early this year! :)
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!
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*).
I love listening to thi s guy, i understand maybe 10% of what he say's, but that's ok because i love science and he does not put me to sleep like some!! lol.Long life to Mr.Susskind her and after.
Its pretty actually of u think of it literally im 13 and i get it and really interested in it!
This is going to be good.
Would it be possible to get the lecture notes of these lectures?
some say he's wonderful, some get bored and switched away, then I have to say I'm gonna read a book even at a rate of 12 pages a day it'll be far better.
Depends on what you are looking for.
Thank yall
Can we not do an observational experiment of a partical of position n momentum at same time to then get both its position n momentum, why can't we observe both simultaneously dule experiment on same partical thus defeat this idea of can't know both, it's one or the other, seams can use a pc to calculate math if take calculations of partical at multiple spots then give position and it momentum...?
You can measure both at the same time. What you can't get is the same values every time you do this measurement. There will be a considerable uncertainty in the statistical distribution of these measurements.
Translation is a symmetry to Dr. Susskind, but not in ordinary language. We earthlings would call it an invariant.
Hardest part is the Leonard Equation, I still haven't solved it.
I love this guy... AMAZING.
This professor's name is Leonard Susskind. I will check him out in CZcams.
Didn't understand this lecture, I have only completed A-level maths is this enough to understand this course?
No
Being stupid, or just not indoctrinated into the notation, there can be nothing but local symmetry on a BB hypothesis. That reduces Bell's violatons of inequalities to a possibly tangible but not universal principle; an epi-phenomenom. I hate to quote Lee Smolin here but:
"One problem with the use of symmetry as a route to unification is that we must then explain why the symmetry is broken. This can make the effective laws which appear to govern our universe contingent- as they are consequences of a particular solution which breaks the symmetry spontaneously. The problem of explaining our observedlaws is then pushed back to a question of initial conditions, because different solutions may lead to different symmetry-breaking patterns.
The limit of this line of thought is string theory, which comes in an infinite number of versions depending, in part, on the symmetry-breaking pattern coded into the geometry of the extra, compactified dimensions."
Taking us into the land of Fae or Fairy, we end up with Big Bounces, Multiverses and 2-dimensions ruling three, the Holographic projection from the boundary. Smolin would like to set up Time as fundamental. Others want the quanta,, It from Bit. As far as I can see, the fundamental theory is Entropy. ENTROPY PROVES GOD; we started out, humanly, as pristine, cosmically as nothing, the infinitesmal if you like, just as in a BB scenario; and we're complexifying, congealing, running down to Absolute Zero, temperature wise. Anyone going to deny that with a CMB at 2.725?
My point is, irrefutable logic, if we're running down we were wound up. Fine-tuning and the Fine-Structure Constant exclude a Goldilock's effect. Even Sir Fred Hoyle realised that, and postulated a then unknown resonance in Carbon. As regards life, over 5,000 enzymes don't just get together in their little warm pond or lagoon to key and lock amino acids. String theorists and evolutionists stretch credibility, my credibility, to beyond breaking point. But what do I know? Anyone can use fairytales, i.e. untestable or/and unbreakable theories, to set up their hypotheses. 2 + 2 doesn't equal 4 in 3-dimensions.
+bin don Just keep in mind that personal interpretation of physics is not physics. If you think "entropy proves god", publish in peer-reviewed journals please. If you cant get published your claim is probably just that - a claim.
I learned that people write short for Albert as Al. For instance; Al Gore for Albert Arnold Gore.
I think Alb is a more proper way than Al.
So basically quantum mechanics is really an intersection between math and physics as you need to I understand vector spaces and symbol operators..
No , i think there's no branch of physics without math. Math is to Physics what words are to language
@@black_jack_meghav that's what I was saying. Math is descriptive.
At last why psi(x+€) is replaced by psi(x-€) ? Displacement was toward right side.
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)
Me: Why are we doing this?
Lenny: You see where we're going, we're making this into a differential equation.
Me: Yes, it is obvious.
favourite thing to sleep to
In 44:48 , what requires this operator to be Hamiltonian? Shouldn't any Harmitian operator be just fine?
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. czcams.com/video/tRWBoossG0Y/video.html could help too.
missing subtitles. You can insert them?
you found a subtitle ?
does the time operator (U(t)) is a symmetry?
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.
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?
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"
great
I am still trying to find out WHY group theory is necessary to do quantum mechanics. Anyone help me?
Edit: His last sentence in the lecture said the symmetries that do not commute with each other have real power …. More to the story I guess. But still wonder why groups are NECESSARY.
Because nature has symmetries and symmetries are causing conserved quantities and in real QM conserved quantities is all you ever care about.
I am 11 years old and i understand none of this
I'm 20 and I barely understand anything.
38 .....huh???
Nancy Witt
that's coz you're 11 years old and are watching videos completely unrelated to your age group XD
Btw, I'm 18
Well I preferred Tom n Jerry to Advanced Quantum Mechanics at the age of 11.
You don't quit it. One day you will get it.
I'm 15 and barely understand some 20% of what he's saying
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!
I suddnely opened the video. Can anyone tell me is it langauge speaking class and which langauge he is writting on the board??
Curious about the choice of words orthogonal versus linearly independent?
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.