Advanced Quantum Mechanics Lecture 7

(November 4, 2013) Leonard Susskind extends the presentation of quantum field theory to multi-particle systems, and derives the particle creation and annihilation operators.

Originally presented by the Stanford Continuing Studies Program.

Stanford University:

Continuing Studies Program:

Stanford University Channel on YouTube:

[sijojosephdr]

Dear Professor,
                         Thank you very much. I had done a course on quantum filed theory five years ago,  but the concepts were not this much clear to me.  I haven't seen anybody with this much clear ideas in small scales and big scales, ( I meant your general relativity course) ! You have enlightened me  with your wonderful lecture and thank you professor Susskind and thank you Stanford for standing for the high quality education !!!

[joabrosenberg]

Particle in a box; Many Particles 15:00; Fock space 18:00; Field Operator 19:00; The field operator is a creation operator which creates a particle at location x 28:00; Psi dagger Psi is a number operator 37:00; Total Energy of a state 44:30; Field energy expectation value 56:00; Joke about mathematicians ... 1:16:00;

[ahmedhass]

Sir u r amazing
thanks for this well illustrative lecture :)

[qbtc]

Around 1:18:00, Susskind posits that Dirac didn't have an ordinary mind and might've been somewhere on the autistic spectrum. Asperger's syndrome might be the more applicable diagnosis if you read the differences.

[Rayquesto]

20:22 So many emojis with actual meaning. Lol

[lordofutub]

Am I right in assuming the energy of a field here is shown for a field with just one kind of particle as merely one psi is used? Or can we see psi as a focks space collection of wavefunctions for multiple particles?

[hasanshirazi]

Field Operator Ψ creates a particle at a certain location.
Creation operator a+ creates a particle at a certain energy level.

[doubleja]

1:07:13 ..Dirac's Car-Rot notation. Thank you for the chuckle good sir.

[zphuo]

@26:00 The state |i> is 1 particle in the i-th energy level. So it equals to a+_i |O>. At the same time the <i|x> is just the complex conjugate of <x|i> which is i-th energy level wave function projected on x...
@36:00 About number of particles u just remember that a+_i a-_i |ni> = N_i |ni> in QFT is unit of number but not the unit of energy level.

[qbtc]

Judging by the questions from the audience, only a fraction really understands what's going on at this point. There are some really bad questions in this lecture and the worst of them is at 1:03:00 when the guy asks Susskind how he did what he has been showing for the past 2 lectures in painstaking detail. God bless Prof Susskind and his infinite patience. I am forever indebted to him for helping me understand QFT and GR - two huge items checked off my bucket list.

[erwinmarschall]

1:16:00 The dual space of a vector-space V consists of all linear functionals on V.
For finite-dimensional V the dual space is isomorphic to V.
The dual of a (infinite-dim.) Hilbertspace is intricate (Wikipedia: Dual space).
E.g. one problem is normalizing  |x>  leading to the square of the delta-fctn !
Mathematicians usually don't accept physicists's (in this case Dirac's) loose handling.

[riveravaldez]

This is awesome. I've never knew that he knows so much about Quantum Mechanics. Chapeau, John Malkovich!

[JT]

You'd think a university would be able to order a playlist correctly :/

[ivanlevtetov]

He is like Rolling Stones in physics. I love his lectures!

[ficolossale]

im a medicine student, but after watching those videos im thinking very seriously about doing this for living

[ddorman]

Thank yooou Lenny, I can ' t wait too talk too you about STUFF !!, Peace and love, Doug :).

[robertwilsoniii]

I never would have expected inferential statistics to help me understand quantum field theory. But all we're doing here is adding up all the averages and then dividing by the number of particles. This is just like estimating or calculating a population total jn statistics. It's just a consequence of the formula for averages.

[Maorio]

Sorry for disliking the video is great but it's always pooping up while I sleep 😭

[jimmyb]

"Just replace the psis by Psis, of bigger size. *sigh*" :D

Best one-liner yet!

[TheVivek]

3:59 "I rather you learn something rather than nothing"