(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to find the 2x2 Hamiltonian matrix for the Hamiltonian, which is written in second-quantized form as below for a system consisting of the electrons and photons.

H = h/ωb†b + E1a†1a1 + E2a†2a2 + Ca†1a2b† + Ca†2a1b,

a's are creation and annihilation operator for electrons, and b's are for photons.

2. Relevant equations

Need to be written in the basis of the following states

|φ1> = 1 √(n−1)! a2† (b†)^(n−1)|0>

|φ2>= 1 √(n)! a1† (b†)^(n)|0>

I'm not sure where to begin. I'm guessing I have to find the eigenvalues and vectors of the hamiltonian but not sure how. Could someone help me start this problem? Thanks.

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# Homework Help: Hamiltonian Matrix?

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