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arXiv quant-ph/03070182003-07-03quant-phcond-mat

Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations

G. Kälbermann

备注：: Latex format, no figures, submitted to journal of physics A
DOI：: 10.1088/0305-4470/37/8/011

英文摘要：

Galilean invariant Schrödinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schrödinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.

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