Advice for first time studying Quantum Mechanics ?

[Ibrahim Hany]

I am studying my first -and only, undergrad speaking- Quantum Mechanics course this term in a Nuclear Engineering Department.

What would be your advice for some one who is first studying quantum mechanics?

I am asking about any advice that would come to your mind when you read the question: how to study, how to think, things I should note that may be intuitively hard to comprehend, expected problems..etc.

Note: Our syllabus started directly by a very short reminder of black body radiation, photoelectric effect & Compton scattering, then we headed to the postulates of the Quantum Theory, and then Schrödinger Equation and solving an infinite well problem! (all that in the first three lectures), then we are expected to do more application on Schrödinger's Equation, and then we will spend some time on Angular Momentum and eventually the Scattering theory.

 

[e.bar.goum]

The most useful interpretation of quantum mechanics to date has been "shut up and calculate".

I think it's pretty sound advice for learning quantum mechanics too. The best way to learn quantum mechanics is to churn through the maths. And I guess to trust in what the mathematics tells you about the solution to whatever problem you're working on. (Provided that you've done the maths right in the first place, I guess).

 

[moriheru]

Trust the mathematics! QM is full of stuff like entaglement and uncertainty that we don't find in classical mechanics so don't stop on the counter intuitiv, just go with the mathematics and you woon't get lost. Sorry seams like a repeated post.

 

[atyy]

My advice is slightly different from shut up and calculate. It is: first read Landau and Lifshitz, then shut up and calculate, then read Weinberg. :) (Don't take that too seriously, but do try to read Landau & Lifshitz some time.)

I would also add, the reason we trust the theory is that it describes everything we see. So check what you calculate against real experiments: Hydrogen spectral lines, Stern-Gerlach, Davisson-Germer, Planck's black body formula, the Aspect experiment etc.

 

[bolbteppa]

a) Read section 1 of Landau on Heisenberg's uncertainty principle.
b) Use Heisenberg + experiment to motivate the existence of a probability distribution in measuring something then formalize the math with the computation on page 1 of this book
http://books.google.ie/books?id=STNNAAAAQBAJ&lpg=PP1&pg=PA1#v=onepage&q&f=false
Use that simple computation & Heisenberg as your motivation for using operators as velocity, momentum etc... vectors as states, density matrices, necessity of infinite dimensional spaces etc...
c) Read the rest of Landau, do not skip anything in ch. 1 until you can recite it off by heart, though the ordering can be changed a bit.
d) Read Landau 1 & 2 (e.g. the sections on optics motivate using e^iS/h in section 6)
e) Always think Heisenberg + Quasi-classical
f) Use the McMahon QM demystified book if you want easy computational examples...
g) Read Goursat for the math (Forsyth's single volume ODE's book beautifully uses Euler's version of Laplace's method to solve the Hypergeometric equation in the same way that Airy etc... are solved in Landau's appendix, Laplace's method is in Goursat)

 

[bhobba]

Landau - superb book - but basic it aren't.

My advice at the beginning level to understand the foundations of QM is to start here:
http://www.scottaaronson.com/democritus/lec9.html

Beyond that, despite the very high esteem I hold Landau in, its not the path I would pursue. That would be QM demystified (highly recommend that book as well) then Ballentine:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

But that's because I am primarily interested in theory. And indeed I am with Scott on this - the rock bottom essence of QM is theoretical - not experimental. But that is me. If you are interested in experiment, and want an approach that emphasises that then the following will likely be a better choice than Ballentine:
https://www.amazon.com/dp/110706399X/?tag=pfamazon01-20

Thanks
Bill

 

[moriheru]

A different advice read Susskind.