- #1

noblegas

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## Homework Statement

The system described by the Hamiltonian [tex] H_0[/tex] has just two orthogonal energy eigenstates, |1> and |2> , with

<1|1>=1 , <1|2> =0 and <2|2>=1 . The two eignestates have the same eigenvalue , E_0:

H_0|i>=E_0|i>, for i=1 and 2.

Now suppose the Hamiltonian for the system is changed by the addition of the term V, given H=H_0+V.

The matrix elements of V are

<1|V|1> =0 , <1|V|2>=V_12, <2|V|2>=0.

a) Find the eigenvalues of the new Hamiltonian, H , in terms of the quanties above

b) Find the normalized eigenstates of H in terms of |1> , |2> and the other given expressions.

## Homework Equations

## The Attempt at a Solution

a) I don't know how to begin this problem but I guess I will start by plugging in the values for H_0 and V: H=H_0+V=<1|1>+<1|V|1>=1+0=1 for the first value of H_0 and the first value of V. don't you find the eigen value by writing out this expression: det(H-I*lambda)=0? I have kno w idea.