Expectation values and operators.

[wads]

i'm just not sure on this little detail, and its keeping me from finishing this problem.

take the arbitrary operator \tilde{p}^{n}\tilde{y}^{m} where p is the momentum operator , and x is the x position operator

the expectation value is then <\tilde{p}^{n}\tilde{y}^{m} >

is this the same as <\tilde{p}^{n}> <\tilde{y}^{m}>?

if not, how would i go about calculating <\tilde{p}^{n}\tilde{y}^{m} >?

 

[CompuChip]

In general, they are not the same. The expectation value of an operator \hat A is
\int \Psi^*(x) \hat A(x) \Psi(x) \, \mathrm{d}x
where \Psi(x) is your wavefunction (assuming you are talking QM here).
In this case,
\int \Psi^*(x) \hat p^n \hat y^m \Psi(x) \, \mathrm{d}x<br /> \neq<br /> \left( \int \Psi^*(x) \hat p^n \Psi(x) \, \mathrm{d}x \right)<br /> \left( \int \Psi^*(x) \hat y^m \Psi(x) \, \mathrm{d}x \right).<br />
You could write out \hat p in the position basis and work out what \hat p^n(y^m \Psi) looks like.