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Homework Help: Ladder operater for momentum space wavefunction (harmonic oscillator)

  1. Oct 25, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to find the momentum space wavefuntion Phi(p,t) for a particle in the first excited state of the harmonic oscillator using a raising operator.

    2. Relevant equations

    Phi_1(p,t)= "raising operator" * Phi_0 (p,t)

    3. The attempt at a solution

    In position space, psi_1 (x) = a+psi_0(x), where a+=1/sqrt(2pi*omega*h-bar)*(-ip+mwx)

    but in position space, x is replaced with i*h-bar*d/dp, and the operator for p is just p.

    I tried inserting the new position operator in a+, but what I get is, what looks like a good solution, multiplied by -i.

    I'm not sure if wave functions can have a factor of i out front (i think the can, please correct me)

    I really just need help formulating this ladder operator in p-space, I can take care of the rest
    Last edited: Oct 26, 2012
  2. jcsd
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