How Do I Find the Energy of a Non-Hermitian Hamiltonian with Bosonic Operators?

[ozlemathph]

Hi all,

There is a Hamiltonian in terms of "a" and "a^{dagger}"bosonic operators H=ω*(a^{dagger}a+1/2)+alpha*a^2+β*a^{dagger}^2 and ω, alpha and β are real constants and its energy is E=(n+1/2)*epsilon where epsilon is ω^2-4*alpha*β. Now, I tried to find this energy but I couldn't. Would you help me please? Thanks.

 

[Matterwave]

When you say "its energy" what do you mean specifically?

For the usual quantum harmonic oscillator, the number states |n> are eigenstates of the Hamiltonian. In this case, they are not. So what states are you trying to find the energies of?

 

[Bill_K]

ozlemathph, The first thing you might wonder about is whether your Hamiltonian is correct. It's not Hermitian!