# Hermitian operator matrix

Lolek2322

## Homework Statement

Eigenvalues of the Hamiltonian with corresponding energies are:
Iv1>=(I1>+I2>+I3>)/31/2 E1=α + 2β
Iv2>=(I1>-I3>) /21/2 E2=α-β
Iv3>= (2I2> - I1> I3>)/61/2 E3=α-β

Write the matrix of the Hamiltonian in the basis of the orthonormalized vectors I1>, I2>, I3>

If in t=0, system is in the state I1>, what is the wave function in t?

Hij = <ilHlj>

## The Attempt at a Solution

Although I know that energy is the eigenvalue of the Hermitian operator, I am not sure how to incorporate that in this certain problem. I have used mentioned equation for previous problems, but I always had the form of the operator. With only eigenvectors and eigenvalues I am stuck and don't even know how to begin solving this.

Last edited:

Mentor
There seems to be a part of the question that is missing. Can you write it out fully?

Lolek2322
There seems to be a part of the question that is missing. Can you write it out fully?
I appologize. I have written it now

Mentor
One way to go about this is to start by writing the Hamiltonian in the |v1>, |v2>, |v3> basis, then applying the proper transformation operation to "rotate" the Hamiltonian to the |1>, |2>, |3> basis.

Lolek2322
But unfortunately I do not know how to do that