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

Calculate the expectation values of x, [tex]x^2[/tex] for a particle in a one dimensional box in state [tex]\Psi_n[/tex]

2. Relevant equations

[tex]\Psi_n = \sqrt{\frac{2}{a}}sin(\frac{n\pi x}{a})[/tex]

3. The attempt at a solution

i formed the integral

[tex]\int_{-\infty}^{+\infty}\Psi ^2 x dx[/tex] as the expectation value of x. (Psi squared simply because this psi is not complex)

this gives [tex]<x>=\frac{2}{a} \int_{-\infty}^{+\infty}x sin^2(\frac{n\pi x}{a})dx[/tex]. The problem is i do not know a way to simplify this integral, similarly i have the problem when there is an x^2 in the integral.

any help would be appreciated

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# Homework Help: Expectation values

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