(adsbygoogle = window.adsbygoogle || []).push({}); problem based on hermitian operator

1. The problem statement, all variables and given/known data

A is an hermitian operator and as we know the eigenstates a of A with eigenvalues a satisfy A psi a = a psi a.

How do we show that lambda psi a (lambda is a non zero complex number) is an eigen state belonging to the same eigen value a. We also need to say whether the eigen value is non degenerate or not.

2. Relevant equations

We know the property of hermitian operator

(-infinity to + infinity) integral phi* A psi dx = (-infinity to + infinity) psi (A phi)* dx

3. The attempt at a solution

(-infinity to + infinity) integral phi* A (lambda psi a) dx =

(-infinity to + infinity) lambda psi a (A phi)* dx

Dont know how to proceed from here.

Regards.

QP.

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# Homework Help: Problem based hermitian operator

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