Why is ⟨x⟩ zero when Ψ is odd?

[Rabbot]

I have a question about expectation values in quantum mechanics.

Since calculating <x>=$\int\Psi*x\Psi$ does x always make this functions odd? If $\Psi$ is odd then $\Psi*$ I would assume is odd as well and then <x> would be odd*odd*odd, if $\Psi$ is even then I again assume it would be even*odd*even. Does an odd function make the whole function odd regardless of the two even functions?

 

[vela]

Yup, if the wave function is even or odd, the integrand will be odd, so the expectation value will be 0.