(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Well I thought this problem was easy, turned in the homework and got it wrong. My prof is hard to get help from, so hopefully someone here can help me out. A particle is in a one dimensional infinite square well with walls at x=0 and x=L. At time t=0 the well is expanded to width 2L. What is the probability the particle will be in the nth stationary state of the expanded well? I bet a lot of people have seen this before apparently it's a pretty popular problem.

2. Relevant equations

[tex]\left\langle\Psi_{f}\left|\Psi_{i}\right\rangle = d_{n} [/tex]

3. The attempt at a solution

[tex]=\frac{\sqrt{2}}{L}\int sin(\frac{n \pi x}{2 L})sin(\frac{\pi x}{L})dx[/tex]

So I'm pretty sure I'm right so far, and the problem is just to evaluate the integral. I was sure the solution was

[tex]d_{n}=\frac{\sqrt{2}}{2} [/tex] if n=2

[tex]d_{n}= 0 [/tex] if n not = 2

But apparently the answer is

[tex] d_{n}= \frac{\sqrt{2}}{2}[/tex] if n=2

[tex]d_{n}= \frac{4}{\pi}\frac{1}{(n^{2}-4}[/tex] if n is odd

[tex]d_{n}= 0 [/tex] otherwise

I can plug the integral into mathematica and of course it gives me the right answer. But I have seen integrals like this hundreds of times in solving PDE's, and they always go like I first thought. What is the difference here? This is causing me a ridiculous amount of cognitive dissonance.

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# Homework Help: Particle in infinite well which is suddenly expanded

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