How to solve generalised eigenvalue problems?

[ngkamsengpeter]

I want to write myself a algorithm to solve generalised eigenvalue problems in quantum mechanics.I know there are a lot of library there that allow me to use it directly but i just want to write my own so that i can learn the mathematics methods that solve the problem...
I don't know how to solve the generalised eigenvalue problems without using existing library in computer...
So anyone has any reference so that i can learn the mathematical methods that solve the generalised eigen value problems??

 

[malawi_glenn]

For discrete sets it is easy, e.g. for spin, then you just do a matrix representation for it and solve its eigenvalue problem, this is done in all introductory linear algebra books and scientific computing books.

For the continuous set, it is more complicated. One has to, in general, solve coupled partial differential equation, which is also outlined in any introductory book in scientific computing.

Please tell us about your background in physics, math and computing and what your aim with all this is maybe we can help you better.

cheers

 

[Matterwave]

It's not simple to solve any general eigenvalue equation, indeed, the time independent Schroedinger equation is in fact an Eigenvalue equation (for the energy-eigenvalues), and only a handful of cases are analytically solvable. A lot of the time, you need to resort to approximations, such as perturbation theory.

 

[Born2bwire]

Take a look at LAPACK and see if they report the source of their algorithms for their generalized eigenvalue routines. The manual gives a description of the general method and they have an extensive bibliography at the end.