1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook