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Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $\bra{x} p > = \exp(ipx/\hbar)/\sqrt{2��\hbar}$. The canonical commutation relation between the momentum and position operators and the Ehrenfest theorem in the free particle case are derived solely from differentiation of the delta function and the form of $\bra{x} p >$., 3 pages

Ehrenfest’s theorem states that as a quantum state evolves in time, the rate of change of the expectation value of momentum is equal to the expectation value of the force. In the familiar ‘‘particle‐in‐a‐box,’’ however, the probability of finding the particle at a wall—the only place where forces act—is zero, so at first glance it appears that the expectation value of the force should vanish for any state, which would violate Ehrenfest‘s theorem. This argument is flawed, however, since the forces at the walls of the box are infinite. We consider the box as a limit of a very deep square well and confirm that Ehrenfest’s theorem emerges safe and sound.

The dissipative forces of classical mechanics can be included in quantum mechanics by the use of non‐Hermitian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. The viscosity coefficient for a nuclear collision is estimated.

Ehrenfest theorem asserts that the quantum mechanical motion of a particle when considered in the expectation value sense should agree with classical mechanics in the correspondence limit. An explicit verification of this result is presented in the one‐dimensional case for motion in an infinite potential well (large quantum number limit) and a brief mention is made of the case of a smooth potential (ℏ→0 limit).

Because of domain considerations for the z component of the angular momentum operator, the time rate of change of the expectation value of the angular displacement φ is not equal to the expectation value of the angular velocity operator. The angular velocity operator is the angular momentum operator divided by the moment of inertia. Ehrenfest’s theorem is obtained for the time rate of change of the expectation value of cos φ and sin φ.