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## Homework Statement

Been struggling with a particular problem that keeps coming up in one of my modules, so i thought i'd see if anyone here can enlighten me.

A Hamiltonian H

_{0}is represented by the matrix:

top row: 3 0 -1

Middle row: 0 a 0

Bottom row: -1 0 3

(Unsure how to display matrices)

where is a dimensionless parameter. Show that (1/√2)(1 0 1) is an

eigenstate of the Hamiltonian and derive its eigenvalue. Find the other

two eigenstates and the associated eigenenergies.

## Homework Equations

n/a

## The Attempt at a Solution

Can find the eigenenergy associated with the eigenstate given to us with relative ease, it has a value of 2eV.

However finding the remaining eigenstates has always puzzled me. Is there easy way to find them? as opposed to learning how to use row operators.

Thanks, John