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Quantum oscillator

  1. Jan 16, 2008 #1
    1. The problem statement, all variables and given/known data

    given a harmonic oscillator initially in a coherent state [alpha(0)>, alpha = pe^(iv) find the state of the system at time t.

    2. Relevant equations

    H = hw/2pi(N+1/2) for harmonic oscillator
    given answer: state at time t = e^(-iwt/2)[alpha(t)>

    3. The attempt at a solution

    i've used the schro eqn to find the state but my answer is only dependant on [alpha(0)> rather than [alpha(t)> i figure i must be setting up the equation wrong but i cant figure out where. i'm not looking for a full solution, just want to know how exactly the coherent state [alpha> will vary in time here. any hints would be appreciated
  2. jcsd
  3. Jan 16, 2008 #2
    i think you have to use just the time evolution operator wich is just:

    and it satisfy UU*=U*U=1 since H is hermitian...
    and go on.
    Note that this kind of potential it is really peculiar since it gives you coherent states.

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