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Given a wave function at t=0, how do you find the wave function at time t?

  1. Oct 24, 2010 #1
    I am given the following:

    A spherically propogating shell contains N neutrons, which are all in the sate

    [tex]\psi[/tex](r,0)=4[tex]\pi[/tex]i[tex]j_{1}[/tex](kr)(3/[tex]\sqrt{34}[/tex][tex]Y^{0}_{1}[/tex]+5/[tex]\sqrt{34}[/tex][tex]Y^{-1}_{1}[/tex])

    at t = 0.

    How do we find [tex]\psi[/tex](r,t)?

    My attempt:

    I have a few thoughts; could you apply the time-independent schrodinger equation to find the energy of the state? If that is the case then you would simply tack on the factor of [tex]e^{-i\omega*t}[/tex]. Then you would know that [tex]\hbar*\omega[/tex]=E. . . . right?
     
  2. jcsd
  3. Oct 24, 2010 #2
    I think that should do it. With the TISE, and the TDSE factor, I think you can it.
     
  4. Oct 25, 2010 #3
    This will do if your state is energy eigenstate. If it is a linear combination of energy eigenstates, then you will have to multiply each term by the appropriate phase factor. In this case summation of the new series to get a closed formula may not be easy.
     
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