(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Expectation values

**Physics Forums | Science Articles, Homework Help, Discussion**