Teaching Yourself Quantum Mechanics and Prerequisites

[bstubbz17]

I know this question has been asked before, so please don't assume I didn't browse the archives. I just want some additional opinions. I have limited experience with quantum mechanics, so assuming that I'm starting from absolute scratch, what would be a good way to teach myself quantum mechanics? By this, I would also like included math prerequisites, science prerequisites...pretty mush a step by step guide to understanding quantum mechanics. All feedback is welcomed and appreciated. Thank you.

Oh, and within the archives someone said that you guys should have a sticky about this topic exactly, and I second the motion...just in case you feel like being an overachiever.

 

[jtbell]

I just want some additional opinions.

In addition to what? What opinions have you seen already? Knowing that might help us avoid simply repeating stuff that you've seen already.

I'm starting from absolute scratch

Does that mean you haven't studied any physics at all? How about math? Do you need to start with basic algebra?

 

[Matterwave]

Go read Feynman's PhD thesis, he outlines his method of doing QM, which is perfectly equivalent to the usual way of doing QM. In fact, it is his method that we usually extend to QED (and QFT? Not sure). =)

 

[arunma]

Hmm...self-study of quantum mechanics is a tricky issue. Sure, it's fun to talk about the philosophy of QM in laymen's terms. But to actually do real QM, you need some physical and mathematical understanding. What are we talking about when you say that you're starting "from scratch?" If you've never done classical physics, then studying QM would be pretty much impossible. If you've got a year of classical physics, you should be good to go.

Mathematically speaking, for a barebones study of QM you'll probably want to know single-variable calculus like the back of your hand, and have some knowledge of differential equations and vector calculus. You'll need to know linear algebra, but if you did any matrices in high school then you can probably pick it up as you go along (one of the appendices in Griffiths' QM book gives a good overview). If you've got this, then you should be able to pick up an intro QM book off the shelf and understand the first chapter or two. You'll want to pay careful attention to the section on the infinite square well. This problem is simple enough that you should be able to solve the Schrödinger Equation and derive the wavefunctions and discretized energies without much trouble. I recommend playing around with the infinite square well problem for a few days to get a good understanding of wavefunctions, boundary conditions, eigenstates/eigenenergies, Fourier expansion of wavefunctions, and time evolution.

Good luck!

 

[jtbell]

Actually, for an introduction to QM at the level of solving Schrödinger's equation for simple one-dimensional systems like the infinite square well ("particle in a box"), you don't need quite that much math. You need to be fluent in algebra, trig and exponential functions, basic differential and integral calculus (including of course trig and exponentials), and be acquainted with complex numbers and the concept of a differential equation.

Moving up to multidimensional systems like the hydrogen atom, you need to know about partial derivatives and multidimensional integration.

On the physics side, for one-dimensional situations you need to be familiar with classical concepts like momentum, energy (kinetic and potential) and the mathematical description of waves. For the hydrogen atom you need to know about angular momentum in addition.

I've taught a second-year "introductory modern physics" course that introduces QM under basically those conditions. It's not nearly as complete or rigorous a presentation as you'd get in a real QM course, but it's intended only as a starting point for further study.