- #1
phrygian
- 80
- 0
Homework Statement
Calculate the general matrix element of the position operator in the basis of the eigenstates of the infinite square well.
Homework Equations
[tex]|\psi\rangle =\sqrt{\frac{2}{a}}\sin{\frac{n \pi x}{a}}[/tex]
[tex]x_{n,m}=\langle\psi_{n}|\hat{x}|\psi_{m}\rangle=\int^a_0\psi^\star_{n} x \psi_mdx[/tex]
The Attempt at a Solution
What I tried doing is substituting the sin eigenfections into the integral and then using the relation that sin(x)sin(y)=(cos(x-y)-cos(x+y))/2 and then integrating from 0 to a. I keep getting a negative answer, am I using the wrong approach? I know this doesn't work when m=n, but shouldn't it work when they aren't equal?
Thanks for the help