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Evolution of wave function

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi, i would to resolve this problem of quantum mechanics.

    I have hamiltonian operator of a unidimensional system:

    [itex]\hat{H}={\hat{p}^2 \over 2 m}-F\hat{x}[/itex]

    where m and F are costant; the state is described by the function wave at t=0

    [itex]\psi (x, t=0)=A e ^{-x^2-x}[/itex]

    where A is a costant.

    How can I calculate the the avarage of x and p at time t after t=0 ( so [itex]<x>_t[/itex] and [itex]<p>_t[/itex] )?

    what is the fast procedure to solve it?

    2. Relevant equations
    [itex]\hat{H}={\hat{p}\over 2 m}-F\hat{x}[/itex]

    [itex]\psi (x, t=0)=A e ^{-x^2-x}[/itex]

    3. The attempt at a solution

    I found a solution but it seems very long and boring...
     
    Last edited: Feb 3, 2012
  2. jcsd
  3. Feb 3, 2012 #2

    Simon Bridge

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    [tex]\psi(x,t)=\psi(x,0)e^{-iEt/\hbar}[/tex]... where E is given by: [tex]\hat{H}\psi=E\psi[/tex]

    note: shouldn't the momentum operator appear squared in that hamiltonian?
     
  4. Feb 3, 2012 #3
    oh yes it's p2/2m... but find eigenvalue E is too hard!
     
  5. Feb 3, 2012 #4

    vela

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    Use the Ehrenfest theorem.
     
  6. Feb 3, 2012 #5

    Simon Bridge

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    Ahhh yes - that's easier.

    You don't have discrete E eigenvalues because you don't have a lower bound - but you don't need them. Sorry, my bad.
     
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