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

[tex]

u(x) = \sqrt{\frac{8}{5}}\left(\frac{3}{4}u_{1}(x)-\frac{1}{4}u_{3}(x)\right)

[/tex]

Determine the time-dependent expectation value of position of this wave function (the particle is in an infinite potential well between x = 0 and x = a).

3. The attempt at a solution

I make it a/2, ie. that the expectation value for this wave function is time-independent - we always expect it at the centre of the well. Does that seem reasonable for that superposition?

On integrating, I end up with three integrals, two of which amount to just the expectation values of the first and third eigenfunction times their respective probabilities (so I say [9/10]*[a/2] + [1/10]*[a/2], without bothering to unpack them) , and one integral which involves the product of u1 and u3 with x times a cosine component. This I evaluate as 0. Hence we have just a/2.

Does that seems stupid to anyone?

Cheers.

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# Homework Help: Expectation value for a superposition

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