Infinite Square Well Frequency of Oscillation

[Blitzmeister]

Homework Statement

Consider a particle in an infinite square well potential that has the initial wave-function:
Ψ(x,0) = (1/√2) [Ψ_1(x) + Ψ_2(x)]

where Ψ_1(x) and Ψ_2(x) are the ground and first excited state wavefunctions. We notice that <x> oscillates in time. FIND the frequency of oscillation

Homework Equations

So,
<x> = expected value integral over 0 to L
Ψ_1(x) = √(2/L) sin(πx/L)e^(-iE/ћt)
Ψ_2(x) = √(2/L) sin(2πx/L)e^(-iE/ћt)

The Attempt at a Solution

I solved:
<x> = [(1/2)-(16/(9π^2))]L
(Not only did I do this by hand but I also checked it against mathematica so this is definitely not wrong)
Real question is, WHAT is the frequency of oscillation actually? I have NO idea what the question is asking.

 

[TSny]

What happened to the exponential time factors. Hint: E is not the same in Ψ_1 and Ψ_2.

 

[Blitzmeister]

Ah so they are different. Okay so what I did, which I guess is wrong was cancel the two exponential time factors since they were e^(-iEt/hbar) and e^(-iEt/hbar)
In that case then still, what exactly is the oscillating frequency? omega?

 

[TSny]

Right, the time factors are different and so they won't cancel. You should recalculate <x>. You will get a time dependence from which you can deduce the oscillation frequency.