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

by Demon117
Tags: function, time, wave
 P: 162 I am given the following: A spherically propogating 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 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?
 P: 647 I think that should do it. With the TISE, and the TDSE factor, I think you can it.
 P: 1,412 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.