Basic Question about Time Dependent Wave Functions

[atomicpedals]

The situation I have in my problem is the standard infinite square well from 0 to L. The normalized eigenfunction is

\phi_n(x) = \sqrt{2/L}sin(n\pix/L) for n=1,2,3,...

if my wave function at time t=0 is then

cos(a)\phi₁(x)+sin(a)\phi₂(x)

is my wave function at more general time t something like

(cos(a)\phi₁(x))*exp(iEt/\hbar)+(sin(a)\phi₂(x))*exp(iEt/\hbar) ?

 

[vela]

Yes, it's something like that, but the E's for the two terms are different.

 

[atomicpedals]

Right, E is dependent on n.