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

by Demon117
Tags: function, time, wave
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Demon117
#1
Oct24-10, 05:14 PM
Demon117's Avatar
P: 165
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?
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jfy4
#2
Oct24-10, 06:42 PM
jfy4's Avatar
P: 647
I think that should do it. With the TISE, and the TDSE factor, I think you can it.
arkajad
#3
Oct25-10, 09:04 AM
P: 1,411
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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