EHRENFESTS THEOREM AND THE PARTICLE-IN-A-BOX

Ehrenfest's theorem states that as a quantum state evolves in time, th e 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 p lace where forces act-is zero, so at first glance it appears that the expectation value of the force should vanish for any state, which woul d 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 the orem emerges safe and sound. (C) 1996 American Association of Physics Teachers.