# Find the eigenvector with zero eigenvalues at any time t from the Hamiltonian

• Jack_11

#### Jack_11

Homework Statement
A Hamiltonian of 3 level system is given by:
Relevant Equations
H= Acos^2 bt(|1><2|+|2><1|)+Asin^2 bt(|2><3|+|3><2|)

I have been asked to find that H has an eigenvector with zero eigenvalues at any time t, but I don't know where to start
I have a question relates to a 3 levels system. I have the Hamiltonian given by:

H= Acos^2 bt(|1><2|+|2><1|)+Asin^2 bt(|2><3|+|3><2|)

I have been asked to find that H has an eigenvector with zero eigenvalues at any time t

Jack_11 said:
Homework Statement: A Hamiltonian of 3 level system is given by:
Homework Equations: H= Acos^2 bt(|1><2|+|2><1|)+Asin^2 bt(|2><3|+|3><2|)

I have been asked to find that H has an eigenvector with zero eigenvalues at any time t, but I don't know where to start

I have a question relates to a 3 levels system. I have the Hamiltonian given by:

H= Acos^2 bt(|1><2|+|2><1|)+Asin^2 bt(|2><3|+|3><2|)

I have been asked to find that H has an eigenvector with zero eigenvalues at any time t

You have to make your best attempt. You must know something about eigenvectors and eigenvalues.