Chapter 4.5, Problem 4.42P

(a)

To determine

The proof that the time derivative of the expectation value of the position vector is $\frac{1}{m}\langle \left(p-qA\right)\rangle$.

(b)

To determine

The proof that the expectation value of the acceleration vector is $q\langle E\rangle +\frac{q}{2m}\langle \left(p\times B-B\times p\right)\rangle -\frac{q^2}{m}\langle \left(A\times B\right)\rangle$.

(c)

To determine

The proof that the expectation value of the acceleration vector obeys the Lorentz force law.