Answer to Question #164615 in Quantum Mechanics for Hima bindu

Question

find the Expectation value of. [xp]-[px] indetail

Answer 1

Answer

Suppose we have any wavefunction

$\psi$ .

Now commutator

$[x, p_x]\psi=xp_x\psi-p_xx\psi$

$=x(-i\hbar \frac{d\psi}{dx}) -(-i\hbar\frac{d(\psi x) }{dx})$

$=-i\hbar x\frac{d\psi}{dx}+i\hbar x\frac{d\psi }{dx}+i\hbar\psi$

$=i\hbar$