Advanced quantum theory, Lecture 1

*UPDATE* lecture notes available at

Many thanks Michael Astwood!

This summer semester (2016) I am giving a course on advanced quantum theory. This course is intended for theorists with familiarity with basic textbook single-particle quantum mechanics. The main objective is to understand how to study many interacting particles within QM. We will cover second quantisation, scattering theory, and some elementary relativistic quantum mechanics.

Here in Lecture 1 I start the study of the configuration space of multiple identical classical particles.

[kockarthur]

25:15 That was the most beautiful board-clearing/erasing I have ever seen.

[accountone]

Thank you so much for this high value content! (I think I will binge-watch your courses)

9:50 Course Outline
14:56 Why QM is hard. The classical limit (22:47 Symmetries)
26:36 Identical particles (Gibbs paradox...)
42:33 Paper
46:36 1D space, N=2 (two particles)
57:13 X=R^n
1:03:30 Example: 2 particles
1:13:39 Configuration space for two particles in R^2

[Rock-szhn]

Amazing to think that to learn any advanced theory 100 years ago, you’d have to go to Uni. Now you just get bored and search it up

[keksnicoh]

this is awesome thank you so much for sharing!

[aliceiqw]

Thanks so much for posting these lectures

[weishanlei]

Dear professor, it would be very helpful if you can provide all the homework assignments and term test questions on some website for ALL of your recorded courses!

[johndavid]

I’m so interested and hypnotized as I watch him clean his chalkboard.

[Shirokazesan]

Can we just get 18 hours of videos of Tobias Osborne exploring his own random observations in detail? Every tangential remark he makes leaves you wanting to know more, but, sadly, it's always out of the scope of whatever he's lecturing on.

[physicsguy]

Dear Dr. Osborne and others,

I believe I've worked out why the picture Dr. Osborne drew at the end of the lecture is a way of identifying x and -x in the plane. If anyone has a simpler explanation, please share!

Start with just a circle and try to identify opposite points. Cut the circle at a point, turning it into a curled string. Move the ends of the string over each other so they overlap a bit. If the length of the overlap is L, then a point a distance x from one end of the string is identified with a point a distance L-x from the other end of the string. Identifying opposite points on the original circle would mean we want a point a distance x from one end to be identified with a point a distance c/2 - x from the other, where c is the circumference of the circle. So we need L to be c/2, which is clearly the case in the picture Dr. Osborne drew.

Doing this for circles of all radii 0 to infinity gives the cone! We can also see that the inner angle of the cone must be 30 degrees from this argument. We know a circle of circumference c in the plane gets mapped to a circle of circumference c/2 wrapped around the cone at a height equal where the distance along the cone is r, the radius of the circle. So therefore we have a right triangle with a hypotenuse r and a distance to the center axis of the cone r/2. So if theta is the inner-angle of the cone, sin(theta) = (r/2)/r = 1/2. theta then must be 30 degrees!

Is this an ok way to think about it?

Thanks!

[achiltsompanos]

Thanks Professor. I have a question: the space X2/~ being open (X1<x2), it's not clear when a particle moving towards the boundary, will reach the boundary since the boundary is not in the space. I am thinking something like Zeno's paradox here. What do you think?

[rv]

11:12:05 - I'm not sure that's the standard definition of "doubly connected". For me, n-connected means roughly that the first n homotopy groups are trivial. Your property seems to be: "the fundamental group has 2-torsion"

[nickpreetic]

Great lecture! I look forward to watching them all as well as your QFT series.
At 45:20 do you mean homeomorphic not isomorphic? Isomorphic usually implies some algebraic structure on the sets

[laautaro]

Hi, I have a question (request), in the Github notes there are no assignments or the 1 excercise per week of the seminar. Can we get them somewhere else?

[physicalanish]

What are the mathematical pre-requisites for this course? Differential Geometry seems to be involved .

[leiladousti]

Dear professor
Thanks for your videos.
I would wonder if you upload assignments and some examples with their solution on website.

[richardguh]

Dear Tobias
I only have a text book(advanced quantum mechanics) writen by Franz Schwabl. Can I use it for this excellent class?

[nouraldein]

Why don't you put the syllabus, lectures notes and the assignments as a pdf files in the description?

[juancarlosdominguezsolis.]

this is qft? or qft for mathematics ? this is a good lecture but this sounds me like a maths part of qft, and so thanks for this material

[fahimullah]

The link to your lecture notes doesn't work. Any new links?

[zeyuancao]

Dear tobias,

This may seem to be stupid but clearly a molecule of O2 and a molecule of my DNA is not identical. Therefore some sort of restriction must be placed on the word "particle" but what sort of restrictions and why them, not others? What do we mean by "particle" exactly?