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 propagating shell contains N neutrons, which are all in the sate

$$\psi$$(r,0)=4$$\pi$$i$$j_{1}$$(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 Schrödinger 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.