Question

Define and give examples of eigenvalues, eigenfunctions and eigenequations.

Answer 1

With regards to the Schrodinger equation.

Answer 2

It would be better to start with a little linear algebra first.

Answer 3

Maybe learning about eigenvectors and eigenvalues of matrices, then apply it to QM

Answer 4

A simple example would be the stationary states of the simple harmonic oscillator. For the math I refer you here:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc2.html