Basic Question about Time Dependent Wave Functions

1. Sep 4, 2011

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$\pi$x/L) for n=1,2,3,...

if my wave function at time t=0 is then

cos(a)$\phi$1(x)+sin(a)$\phi$2(x)

is my wave function at more general time t something like

(cos(a)$\phi$1(x))*exp(iEt/$\hbar$)+(sin(a)$\phi$2(x))*exp(iEt/$\hbar$) ?

Last edited: Sep 4, 2011
2. Sep 4, 2011

vela

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

3. Sep 5, 2011

atomicpedals

Right, E is dependent on n.