# Quantum Mechanics Superposition Question

1. Feb 13, 2012

### jumbogala

1. The problem statement, all variables and given/known data
A particle in an infinite square well has as its initial wavefunction ψ(x,t=0) = (1/√2)[φ1 + φ3].

Find |ψ(x,t)|2. Express it as a sinusoidal function of time using ω= π2*h/(2mL2).

2. Relevant equations
Note that φn = √(2/L)*sin(nπx/L) for a well of width L.

3. The attempt at a solution

I found something in my book which says that ψ(x,t) = Ʃbn*e-iωntφn.

Therefore, my ψ(x,t) = (1/√2)[e-iω1t)φ1 + e-iω3t)φ3].

Is that right so far?

Then, I can compute |ψ(x,t)|2, but I don't see how that is going to give me an answer in terms of ω. I have ωn though.

2. Feb 14, 2012

### vela

Staff Emeritus
How are $\omega$ and $\omega_n$ related to the energy of state n?

3. Feb 16, 2012

### genericusrnme

When you say you found something in your book that says $\Psi (x,t) = \sum_n b_n\ e^{-i\ \omega _n \ t}\ \psi _n(x)$, do you know what that is?
Also, do you know what $\omega _n$ actually is?

Last edited: Feb 16, 2012