Phy5645/HO problem1

Calculate the expectation value of x in eigenstate.

Solution:

We can compute the expectation value of x simply.

$\langle \Psi _{n}|x|\Psi _{n}\rangle =sqrt{frac{\hbar }{2m\omega }}$

We should have seen that coming. Since each term in the operator changes the eigenstate, the dot product with the original (orthogonal) state must give zero