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Sudden perturbation approximation for oscillator

  1. May 14, 2008 #1
    1. The problem statement, all variables and given/known data

    An oscillator is in the ground state of [tex] H = H^0 + H^1 [/tex], where the time-independent perturbation [tex] H^1 [/tex] is the linear potential (-fx). It at t = 0, [tex] H^1 [/tex] is abruptly turned off, determine the probability that the system is in the nth state of [tex] H^0 [/tex] .


    2. Relevant equations

    First, since the perturbation is turned off abruptly, the sudden perturbation approximation may be used.

    [tex]P(n) = |<n|n^0>|^2[/tex].


    3. The attempt at a solution

    I am not sure where to start. Is this best done in the coordinate basis or the energy basis?

    In either basis, I need some type of representation of |n> but I am not sure where to start with that.

    [tex]n^0$[/tex] can be represented as |0> in the energy basis or [tex] \psi(t) = A_0 * e^{y{2}}$ [/tex] in the coordinate basis.

    jsc
     
  2. jcsd
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