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Exceptation of energy by Hamiltonian

  1. Jun 30, 2014 #1
    Hello,

    The question says that we can write the Hamiltonian of the harmonic oscilator like this:
    H=0.5*[P^2/m + (4*h^2*x^2)/(m*σ^4)] where h is h-bar

    I need to calculate the expectation value of energy of the oscilator with the next function: ψ(x)=A*exp{-[(x-bi)^2]/σ^2}.

    I tried to the the integral: ∫ψ*Hψdx where H is the operator of p and x but I got a big integral and I dont think its the write way because the finite answer is pretty simple:
    Answer: (h^2/m)*(1/σ^2 + (2*b^2)/σ^4) where h is h-bar

    How can I solve it?
    Thanks
     
    Last edited: Jun 30, 2014
  2. jcsd
  3. Jul 1, 2014 #2

    king vitamin

    User Avatar
    Gold Member

    I'm not sure there is a simpler way. Could you show us some of your work?

    Also, you could consider a clever change of variables in the integrals (recall that you need to determine the constant A as well).
     
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