# Infinite Square Well Frequency of Oscillation

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1. Oct 12, 2015

### Blitzmeister

1. The problem statement, all variables and given/known data
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

2. Relevant 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)

3. 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.

2. Oct 12, 2015

### TSny

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

3. Oct 12, 2015

### 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?

Last edited: Oct 13, 2015
4. Oct 13, 2015

### 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.