Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Gold Member

    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


    User Avatar
    Science Advisor

    ozlemathph, The first thing you might wonder about is whether your Hamiltonian is correct. It's not Hermitian!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Quadratic Hamiltonian Energy
  1. Hamiltonian and energy (Replies: 3)