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Quadratic Hamiltonian Energy

  1. Jun 4, 2012 #1
    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.
  2. jcsd
  3. Jun 4, 2012 #2


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    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?
  4. Jun 5, 2012 #3


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