How to find the energy level if a three state system

[Zachary Nichols]

I'm having trouble figuring out how to derive a Hamiltonian for a three state system. I know how to for two state system but for a three state I don't know what vectors I could use to derive the operator. Could someone explain how to do it and give a link to somewhere I read about it

 

[atyy]

The Hamiltonian of a system is postulated, not derived.

Given a Hamiltonian, one may ask what the energy levels are.

An example is given in http://massey.dur.ac.uk/resources/gtpurves/gtp_thesis/Ch3.pdf.