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

[Demon117]

I am given the following:

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

\psi(r,0)=4\piij_{1}(kr)(3/\sqrt{34}Y^{0}_{1}+5/\sqrt{34}Y^{-1}_{1})

at t = 0.

How do we find \psi(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 e^{-i\omega*t}. Then you would know that \hbar*\omega=E. . . . right?

 

[jfy4]

I think that should do it. With the TISE, and the TDSE factor, I think you can it.

 

[arkajad]

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.