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Quantum Harmonic Oscillator

  1. Oct 10, 2008 #1
    1. The problem statement, all variables and given/known data
    H = p^2/2m + (kx^2)/2 - qAx (THis is a harmonic potentional with external electric force in 1D)

    |0, A=0 > = |0>_0 for t=0 (ground state)
    |0, A not 0 > = |0> for t=0 (ground state)

    2. Question
    1. Find the probability of being in the state |0, A not 0> for t>=0 when you are in the state |0>_0
    2. Find the coefficients for the station |0>_0 = Sigma_k c_k |k>

    3. The attempt at a solution
    P = |<0, A not 0|e^(-iE_0t)|0, A=0 >|^2 = <0, A not 0||0, A=0 >^2 = ? (how to find this, do i go over to position representation?)
    i've tried that but got an answer which didn't depend of t??? since t factor is being cancelled out by the complex conjugation.

    2. c_k = < k | | 0 >_0 = ?
    Last edited: Oct 10, 2008
  2. jcsd
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