What math do I need to know in order to understand quantum mechanics?

Question

By 'understand' I mean be able to work with equations to model systems and make predictions.

Answer 1

Yes to most of the above, except the one dolt (we all know which one I mean). You'll also need to get some Calculus of Variations under your belt, and some Functional Analysis. The Bessel functions, etc. are all usually included in something called "Special Functions" or as one the above mentions, "Orthogonal Functions".

A good text with all this crap in it is the one by Arfken. I forget the title, but if you ask your prof, I'm sure he'll know the one I'm talking about.

Answer 2

You need to study Niels Bohr who was a proponent of quantum mechanics and if you dont find any error in it ;then, it would be worthwhile to study the Theory.
If you find its flawed as Einstein discovered that ,than you should try to develop a more real theory. It is possible to develop theory with simple algebra or even simple calculus.
You need to come up with a
realistic concept then you may have a Unification equation which after the science commitee comes to Understand it ;they will award you the Nobel Prize Posthumously.

Answer 3

You basically need to be able to solve the Schrodinger equation which is a partial differential equation. So you will need to be able to solve partial differential equations by using separable equations. Knowledge of Bessel functions, spherical harmonics, and Legendre polynomials will help.

Answer 4

you need to know multivariable calculus,
you need to know how to solve partial differential equations
and you need to know the fundamentals of fourier analysis (because you'll be working in hilber space) and linear algebra.

once you know these, you can do the easy stuff.
pick up an easy introduction book. i recommend griffith's quantum mechanics. it's nice and clear.

still. it may be easier to take a class and have someone explain what the important bits are...

good luck

Answer 5

Linear algebra (esp, finding eigenvalues and eigenvectors), multi-variable calculus (changing differential operators to new coordinate systems), ordinary and partial differential equations (esp. separation of variables techniques), orthogonal expansions (esp. orthogonal polynomials), and the basics of inner product spaces (Hilbert spaces). You will learn some pertubation theory while studying it.