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 H0 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.
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.