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QM- Expectation value+Momentum.

  1. Jan 2, 2012 #1
    1. The problem statement, all variables and given/known data
    [tex]{\Psi (x,t)} = \frac {m \omega}{\pi h_{bar}}^{1/4}e^{- \frac {m \omega}{2h_{bar}}(x^{2}+ \frac {a^2}{2}(1+e^{-2i \omega t}+\frac {ih_{bar}t}{m}-2axe^{-i \omega t})}[/tex]

    Problems: Find |ψ(x,t)|2
    Compute <x> and <p>


    2. Relevant equations
    [tex]{x = \int^\infty_{-\infty} x | \Psi (x,t)|^{2} dx}[/tex]
    [tex]{p = -ih_{bar} \int (\Psi^{\star} \frac {\partial \Psi}{\partial x}) dx}[/tex]



    3. The attempt at a solution
    I think eventually I'll be able to find the complex conjugate by just working through it. The problem really arises when I would go into integrate. I tried using Euler's rule (e^ix=isinx+cos) on the the two exponentials in the exponential in the wave function (e^-2iωt and e^-iωt).

    Even after doing that, I see no way to integrate this wave-function! Any help would be appreciated on this problem.
     
  2. jcsd
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