Probability distribution for superposition of two potential well states

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Epideme
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Homework Statement


The stationary Schrödinger equation for a particle moving in a potential well has 2 solutions
psi_1 (x) = e^(-ax^2), with Energy, E_1, and
psi_2 (x) = xe^(-ax^2) with Energy, E_2.

At t = 0 the particle is in the state
psi(x) = psi_1(x) + psi_2(x)

a)Calculate the probability distribution for the particle as a function of time
b)Find the time at which the probability distribution returns to the initial value


Homework Equations





The Attempt at a Solution


Again no progress on this one, i have no idea, thank you in advance for any help offered.
 

Discussion

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of course one always have ideas, come on, you can atleast try to find the equations which you think are relevant and say what you DO think you understand and what you dont't. Just saying "i have no idea" will not help you. You HAVE to give attempt to solution if you want help here.

Hint: Look for time evolution, how is time evolution implemented in quantum mechanics? Look through your books and notes. How do we make a time independent state to become time dependent?