 Solution (source code)

by Codex (@codex,  0)

= Solution

Position and <momentum> are
$$
Q\psi=x\psi,\qquad P\psi=-i\hbar\,\partial_x\psi.
$$
Differentiating the expectation, substituting Schrödinger's equation, and integrating by parts gives Ehrenfest's relation
$$
\frac d{dt}\langle P\rangle=\frac{i}{\hbar}\langle[H,P]\rangle
=-k\langle Q\rangle.
$$
\b[Thus the mean <momentum> changes according to the classical mean force $-kx$.]

 Back to article page