I fell asleep with another TH-cam video and I woke up 20 min ago to this video. I don't know how I got here, just know now I have 20 min watching this dude and finally feel awoke enough to acknowledge it
For anyone interested, minute 45:00 is essentially the mathematical proof of how you can decompose ANY Hermitian operators into the pauli sigma operators, where in the video Sx is actually the Pauli-x gate, Sy is the Pauli-y gate, Sz is the Pauli-z gate and Identity is the identity/idle (id) gate. It's something that is immensely useful when working with Quantum Circuits and the entirety of Quantum Evolutions using unitaries and hamiltonians, and not really explained much in most books. Hope you like it!
This lecture by professor Zwiebach at MIT is very clear and to the point about Dirac notation for matrix mechanics in quantum mechanics. Do not believer the topic could be made any clearer. Great lecture. Learn a lot....
***** i think most people that get confused by dirac notation aren't confused as much by the notation, but by its existence; by that, i mean that it is just one more thing for them to remember and sometimes that can seem more overwhelming than it need be.
Steve Murray Absolutely. Takes time to distinguish between operators and eigenvectors or eigenfunctions as matrices or column or row vectors respectively. Thanks for your input.
Absolutely right. For a long time I thought they were one in the same, eigenvectors and eigenfunction. Now I know the difference. Thanks Steve for getting back in touch.
i love this guy. i originally didnt like his voice but ive began to love it. Ive never seen concepts explained so clearly and coherently. He also sounds like admiral general adam from the movie the dictator. Dont take this the wrong way as both these voices are legendary. Jokes aside thank you MIT for all these free lectures theyve changed my life and education.
Tears of joy in my eyes! Thanks Barton Zweibach! You are the best! I was really having a hard time solving a problem, related to (n . sigma), I knew the notation was shitty, but my professor insisted there was nothing shitty about it, and did not explain anything about the shit at all. Thanks to Barton Zweibach, I now know all the shit about (n . sigma)!
I think that an electron has shift in coordinate (1/2π)msλ in r-direction. (ms:spin quantum number, λ:wave-length) Accordingly, the angular momentum is {r+(1/2π)msλ}p=rp+(1/2π)msλp=rp+ms(h/2π)=L+S. (De Broglie equation: p=h/λ) And the magnetic moment is (area)･(electric current)＝{πr 2+2πr･(1/2π)msλ}･(q/m)p/(2πr)=(q/2m)pr+2(q/2m)ms(h/2π)= (q/2m)L+2(q/2m)S. Thus, we can know that the g-factor for spin angular momentum is equal to 2. I'm sorry that I'm not good at English.
@@falcodarkzz Might be his accent, you have to focus more to understand what he says, so you will remember what he says. And he speaks slowly so you have time to focus.
What is the take-home of 1:04, if we can form the X-State as a linear combination of the Z-state, doesn't that mean the X-State is dependent and not orthogonal to the Z-State? I thought we just went through a bunch of work to force it to be orthogonal.
At the very end, he multiplies the negative eigenstate times -exp(-i phi) to get a resulting form that is nicer when theta = 0. However, the first form is nicer when theta = pi/2 and phi = 0, so you cannot win !
I'm struggling with the concept of basis states here. Why do we need 2 basis states to describe an electron? If we know that z+ component of an electron's spin is 0.9, then we also know that the z- component must be 0.1, no? Specifying the second component seems completely redundant. Furthermore why z+ and z- are said to be orthogonal? They don't seem to be independent at all. Or maybe the idea is that a linear combination of these two z+ z- basis states can be used to describe spin of other things/particles, which are not a single electron?
(This may have a chance of being wrong, so please fact check before quoting me) When you say z+ = 0.9 and z- = 0.1, you are assuming them to be scalars, which they are not. These are wavefunctions, i.e. these are functions of certain variables.
Some of the kids ask some really good questions and point out matters which you don't immediately think of when doing the decomposition, wish I could hear what they were saying. In most OCWs they're always muffled or inaudible.
Sometimes the instructors do not warn us that they take questions from students in class. Without warning, there is no microphone set to handle audio from the students. In those cases, we try to also get the instructors to repeat questions asked in class. Very few instructors remember to do this. Sorry, sometimes it's the best we can do at that time. ¯\_(ツ)_/¯
Because he want to factor out s(z) component , to find out relation between s(x) and s(y) only , by doing so he end with two matrix either one of them will be the s(x) and other will be s(y) with odds one/root(2)..
It's just a fancy way of saying it acts by way of simple matrix-vector multiplication: (A, v) -> Av. One could define other "unnatural" actions of the space of matrices on that vector space as (A, v) => f(A)v, where f is any nontrivial automorphism on that space of matrices as a multiplicative group.
Because spin is the thing which gives the electron magnetic moment in stern gerlach experiment which would normally be given by angular momentum so i think that's the reason we compare them at least that's my guess
For the life of me, I don’t understand this: What do Sx, Sy, and Sz have to do with ANYTHING? He was doing a great job explaining the equations, then suddenly he catapulted us into S world. Why?
And we want a million dollars to capture even more content for the the world... lets talk! ;) j/k Transcripts of this course and lecture notes for this course are available on MIT OpenCourseWare at ocw.mit.edu/8-05F13. Best wishes on your studies!
this is insane the amount of detail he goes into. What a great resource. Thank you MIT and Dr Zwiebach
Absolutely amazing a lecture! He is making things crystal clear.
I fell asleep with another TH-cam video and I woke up 20 min ago to this video. I don't know how I got here, just know now I have 20 min watching this dude and finally feel awoke enough to acknowledge it
For anyone interested, minute 45:00 is essentially the mathematical proof of how you can decompose ANY Hermitian operators into the pauli sigma operators, where in the video Sx is actually the Pauli-x gate, Sy is the Pauli-y gate, Sz is the Pauli-z gate and Identity is the identity/idle (id) gate. It's something that is immensely useful when working with Quantum Circuits and the entirety of Quantum Evolutions using unitaries and hamiltonians, and not really explained much in most books. Hope you like it!
This lecture by professor Zwiebach at MIT is very clear and to the point about Dirac notation for matrix mechanics in quantum mechanics. Do not believer the topic could be made any clearer. Great lecture. Learn a lot....
Absolutely correct. It truly simplifies thing. Thanks for your opinion.
***** i think most people that get confused by dirac notation aren't confused as much by the notation, but by its existence; by that, i mean that it is just one more thing for them to remember and sometimes that can seem more overwhelming than it need be.
Steve Murray Absolutely. Takes time to distinguish between operators and eigenvectors or eigenfunctions as matrices or column or row vectors respectively. Thanks for your input.
Absolutely right. For a long time I thought they were one in the same, eigenvectors and eigenfunction. Now I know the difference. Thanks Steve for getting back in touch.
i love this guy. i originally didnt like his voice but ive began to love it. Ive never seen concepts explained so clearly and coherently. He also sounds like admiral general adam from the movie the dictator. Dont take this the wrong way as both these voices are legendary. Jokes aside thank you MIT for all these free lectures theyve changed my life and education.
This is amazing, honestly helped so much with quantum mechanics course. Shows the difference a lecturer can make.
I can't thank you enough for these lectures. It's just that I can't understand my teacher sometimes and this channel comes to save my life.
I see a lot of positive comment directed at professor Zwiebach, but the real all star is the camera person. The camera person did an excellent job.
Tears of joy in my eyes!
Thanks Barton Zweibach! You are the best!
I was really having a hard time solving a problem, related to (n . sigma), I knew the notation was shitty, but my professor insisted there was nothing shitty about it, and did not explain anything about the shit at all.
Thanks to Barton Zweibach, I now know all the shit about (n . sigma)!
55:18 shout out to the cameraman who actually pays attention 🎉
Seems so trivial now. I wish I had this 20 years ago. Great lecture
Thanks for this class, Professor! Really thanks. It was the best explanation I've seen in years! Congratulations
very detail lectures yet every single word he explained are crystal clear...tnx & ❤ MIT,Tnx & ❤ Dr.Zwiebach.!!❤❤❤🇧🇩🇧🇩
He is such a good teacher.
This lecture was awesome!!, I totally got some things neither my professors or books talked about in detailes. Thank you very much ;D
Whoever transcribes this, the symbol at 35:30 to 35:40 is the Levi-Civita symbol.
55:30 - they're Pauli matrices, not poly or power matrices.
Good catch! Thanks for your comment. We've updated the captions with your feedback.
41:00 is the most hand-wavey thing I have ever heard -> "remove something to do with the identity because otherwise Si will commute with everything"
I think that an electron has shift in coordinate (1/2π)msλ in r-direction. (ms:spin quantum number, λ:wave-length)
Accordingly, the angular momentum is
{r+(1/2π)msλ}p=rp+(1/2π)msλp=rp+ms(h/2π)=L+S. (De Broglie equation: p=h/λ)
And the magnetic moment is
(area)･(electric current)＝{πr 2+2πr･(1/2π)msλ}･(q/m)p/(2πr)=(q/2m)pr+2(q/2m)ms(h/2π)= (q/2m)L+2(q/2m)S.
Thus, we can know that the g-factor for spin angular momentum is equal to 2.
I'm sorry that I'm not good at English.
great work by the camera man 🎥; done a really great job in this video 👍🏻
I find these lectures much better than the ones by alan adams.
Definately. Can't put my finger on why, I just recall what Barton says a lot more.
I feel like he does harder math too
@@falcodarkzz Might be his accent, you have to focus more to understand what he says, so you will remember what he says. And he speaks slowly so you have time to focus.
This prof and course is much more rigorous and mathematically oriented. Alan Adams was more intuitive and very messy.
Could not be clearer!!! Thank you!!
...que aula maravilhosa!
What is the take-home of 1:04, if we can form the X-State as a linear combination of the Z-state, doesn't that mean the X-State is dependent and not orthogonal to the Z-State? I thought we just went through a bunch of work to force it to be orthogonal.
this prof is so good
He is from my university in Peru, in his career he used to get the highest and perfect marks
That look 48:38
1:13:18 there are missing \hbar/2 at the antidiagonal terms.
Great lesson
Who needs Indian man on youtube when you have Peruvian man from MIT
At the very end, he multiplies the negative eigenstate times -exp(-i phi) to get a resulting form that is nicer when theta = 0. However, the first form is nicer when theta = pi/2 and phi = 0, so you cannot win !
thankyou so much!
I'm struggling with the concept of basis states here. Why do we need 2 basis states to describe an electron? If we know that z+ component of an electron's spin is 0.9, then we also know that the z- component must be 0.1, no? Specifying the second component seems completely redundant. Furthermore why z+ and z- are said to be orthogonal? They don't seem to be independent at all. Or maybe the idea is that a linear combination of these two z+ z- basis states can be used to describe spin of other things/particles, which are not a single electron?
(This may have a chance of being wrong, so please fact check before quoting me)
When you say z+ = 0.9 and z- = 0.1, you are assuming them to be scalars, which they are not. These are wavefunctions, i.e. these are functions of certain variables.
Some of the kids ask some really good questions and point out matters which you don't immediately think of when doing the decomposition, wish I could hear what they were saying. In most OCWs they're always muffled or inaudible.
Sometimes the instructors do not warn us that they take questions from students in class. Without warning, there is no microphone set to handle audio from the students. In those cases, we try to also get the instructors to repeat questions asked in class. Very few instructors remember to do this. Sorry, sometimes it's the best we can do at that time. ¯\_(ツ)_/¯
You can turn on the captions
QM cannot be clearer. Any thanks will be less to Dr. Barton Zwiebach and MIT
A great teacher! Thanks!!!!
Thanks ❤️🤍
Great lecture!!
“The h bars over two HAPPILY go out.”
Do they, Dr. Zwiebach?
I sense conflict between them.
Maybe they’re ...
TENS-OR.
what does he mean by accounting procedure in 1:07:26 ? does anyone know?
When deriving the Sx and Sy matrices, why did the professor subract (C+D)Identity?
Did you figure this out? I'm confused about this too.
Because he want to factor out s(z) component , to find out relation between s(x) and s(y) only , by doing so he end with two matrix either one of them will be the s(x) and other will be s(y) with odds one/root(2)..
Small mistake when going through the working finding the determinant. He missed the hbar on the sin theta terms too. Its clarified in notes anyway
Thank you, very helpful!
Play it at 1.25x the normal speed.
1.5x works best for me
Ikr ?? It’s so much better
Make that 0.10 for me please :D
12:54 For a moment, I thought someone would reply “shut up and calculate” 😉
Any good lecture on abstract algebra
What does it mean if a matrix acts naturally on a component vector?
It's just a fancy way of saying it acts by way of simple matrix-vector multiplication: (A, v) -> Av.
One could define other "unnatural" actions of the space of matrices on that vector space as (A, v) => f(A)v, where f is any nontrivial automorphism on that space of matrices as a multiplicative group.
It just transform it to another vector.. in when vector not transformed but scaled by lambda we call that eigen vector of that transformation
angular momentum operators are quite different from spin matrices then why to compare them .....
Because spin is the thing which gives the electron magnetic moment in stern gerlach experiment which would normally be given by angular momentum so i think that's the reason we compare them at least that's my guess
thank you
How do we know that there aren't multiple spin states that have the same eigenvalue?
24:52
Can someone tell me the name of the tensor: Epsilon_ijk?
Levi-Civita Tensor
For the life of me, I don’t understand this:
What do Sx, Sy, and Sz have to do with ANYTHING?
He was doing a great job explaining the equations, then suddenly he catapulted us into S world.
Why?
You just now start using Dirac notation?
I believe it's an introductory course on qm 2.
So the "operator" is a spectator as both 🤔
Why spin ½ is a two dimensional Vector space ....?
Bcz we need only 2 basis(up and down) to describe the state. So 2 dimensional
i want pdf of this lecture
And we want a million dollars to capture even more content for the the world... lets talk! ;) j/k Transcripts of this course and lecture notes for this course are available on MIT OpenCourseWare at ocw.mit.edu/8-05F13. Best wishes on your studies!
Apprentice should have been apparatus, (grand children distraction). Below
Short lecture
This is helpful ❤️🤍
20:42