# Dirac Notation Eigenvalues

## Homework Statement

I have the following question (see below)

## Homework Equations

The eigenvalue equation is Au = pu where u denotes the eigenstate and p denotes the eigenvalue

## The Attempt at a Solution

I think that the eigenvalues are +1 and - 1, and the states are (phi + Bphi) and (phi-Bphi)
however I got this by just substituting these in from the symmetry of the operator.

Is there are neat algebraic way to work out the eigenvalues and eigenfunctions as opposed to just substitution?

I am stuck on working out how to express the 0 eigenvalue eigenstates in terms of the projection operator as well ...

Thank you very much

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