Quantum mechanics and expectation values.

[Rabbot]

I have a question about expectation values in quantum mechanics.

When 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?

 

[Bill_K]

In the two cases you mentioned, Ψ odd or Ψ even, like you say Ψ*Ψ will be even and you'll get <x>=0. However what if Ψ is neither odd nor even? If, for example, Ψ is a Gaussian centered at x = x₀ then you'll get <x> = x₀ ≠ 0.