I have taken a course in spectral theory, l have learned about self adjoint,compact, closed ...operators and how to find there spectrum especially in the case of Schrödinger operator.
But I am curious to know why are we interested in determining the spectrum, what does these eigen values represent?
I will be thankful if any one could explain briefly.
The larger the total dimension of the eigen sub-spaces, the more the matrix of the endomorphism will be simple (i.e. with many zeros), and the more the behavior of that endomorphism will be simple to apprehend (it is a $\lambda$-homothety on the $\lambda$ eigen sub-space).