(adsbygoogle = window.adsbygoogle || []).push({}); 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)[φ_{1}+ φ_{3}].

Find |ψ(x,t)|^{2}. Express it as a sinusoidal function of time using ω= π^{2}*h/(2mL^{2}).

2. Relevant equations

Note that φ_{n}= √(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) = Ʃb_{n}*e^{-iωnt}φ_{n}.

Therefore, my ψ(x,t) = (1/√2)[e^{-i}ω_{1}t)φ_{1}+ e^{-i}ω_{3}t)φ_{3}].

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 ω_{n}though.

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# Quantum Mechanics Superposition Question

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