The Hamiltonian of a system has the matrix representation
H=Vo*(1-e , 0 , 0
0 , 1 , e
0 , e , 2)
Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian (e=0)
when unperturbed the Hamiltonian will reduce to Vo* the 3x3 matrix with 1,1,2 along the diagonal. the eigenvalues are therefore Vo,Vo,2Vo (right??)
I am a bit confused about how to calculate the eigenvectors. I have tried looking this up but still get confused. Would they not all be zero since if you sub the eigenvalue Vo back into matrix you would get for the first row
Vo(1-Vo,0,0) * (x,y,z) = (0,0,0) where (x,y,z) is a vertical matrix???