Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations

Details Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations

2003-07-03

arxiv.org/abs/quant-ph/0307018v1

Physics

Quantum Physics

Latex format, no figures, submitted to journal of physics A

Scientific paper

Galilean invariant Schr\"odinger 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 Schr\"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.

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