Expectation of position in a 2D system

[staraptor]

How does on calculate the expectation of the position operator x in a 2D infinite potential well (in the xy plane)? Do we only work with the Psi to the Hamiltonian in that particular coordinate when finding <Psi|x|Psi>?

 

[vela]

You calculate
$$\langle x \rangle = \iint \psi^*(x,y)\,x\,\psi(x,y)\,dx\,dy$$

 

[staraptor]

Could you explain this please? Where does the double intergral come from?

 

[vela]

What does your textbook say about calculating an expectation value?