Prereqs for undergrad Quantum Mechanics

[physiker99]

Hello,
I will be taking undergraduate level Quantum Mechanics this year. I do not want to face any problems due to required background on maths and physics. I took differential equations and Linear Algebra and I want to make some revisions before semester starts. Where do you think I should start? I mean what are the topics from these courses that really matter in Quantum Mechanics? Also, what about calculus? I am not sure if I really remember final chapters of Multivariable calculus. (Green's, Gauss' etc)

 

[Monocles]

Linear algebra is the most important thing to be familiar with. You want to be very comfortable with what eigenvalues and eigenvectors are - and not just their definitions, but having an intimate understanding of the concepts behind them and why they are important.

You won't need to worry about multivariable calculus - single variable is enough, and any calculus you do will be very simple (basic integration). Knowing the very basics about differential equations helps, but isn't absolutely necessary.

 

[Someone1987]

For differential equations, probably the most important topics for undergrad quantum are

1. Solving second order linear differential equations
2. Solving first order differential equations (just separating variables)
3. Solving partial differential equations (separation of variables--- different than the technique I mentioned in 2).
4. Fourier Series

For linear algebra

1. Understanding what a basis is and how to expand vectors in a basis.
2. Review vector spaces
3. Finding eigenvalues and eigenvectors
4. How to change from one basis to another.

There are probably some others that I am leaving out but these are the most important ones that I can list off the top of my head. Being familiar with these topics, you should be just fine.

In terms of calculus, you just need to know partial derivatives and multiple integrals. I don't think you will need too much vector calculus.