Time-Dependent Wave Function of Spherical Harmonics

[Matea112]

Homework Statement

In t=0, wave function of the particle that moves freely on the surface of the sphere has the wave function:

Ψ(Φ,θ) = (4+√5 +3√5cos2θ)/(8√2π)
what is time-dependent wave function?

Homework Equations

Spherical harmonics

The Attempt at a Solution

I tried normalizing this wave function and got (2π)^¼. I don't think that is right. Was I even supposed to normalize this function?. Regardless of normalization, I don't know how to proceed.

 

[pasmith]

Do you have a general solution for the wave function in terms of a series of spherical harmonics?

Do you know how to determine the coefficients in that series given an arbitrary initial condition?