Hamiltonian Commutator: Finding [H,P_x] for Polarization Operator

[v_pino]

Homework Statement

How do I obtain [H,P_x]? P_x is the polarization operator.

Homework Equations

$$H=-\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial x^2}+V(x)$$

$$P_x=2Re[c_+^*c_-]$$

The Attempt at a Solution

I know how to commute H and x. But somehow can't think of a way to do the same for H and P_x.

 

[ardie]

write P_x instead of x; then do the commutation just as you do for x