Ehrenfest’s theorem and the particle‐in‐a‐box
作者:
D. S. Rokhsar,
期刊:
American Journal of Physics
(AIP Available online 1996)
卷期:
Volume 64,
issue 11
页码: 1416-1418
ISSN:0002-9505
年代: 1996
DOI:10.1119/1.18367
出版商: American Association of Physics Teachers
关键词: QUANTUM MECHANICS;EXPECTATION VALUE;EIGENSTATES;BOUNDARY CONDITIONS;SQUARE−WELL POTENTIAL;BOX MODELS;WAVE FUNCTIONS;SEMICLASSICAL APPROXIMATION;MATRIX ELEMENTS;03.65
数据来源: AIP
摘要:
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.
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