Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations

G. Kälbermann

doi:10.1088/0305-4470/37/8/011

Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations

G. Kälbermann^*

^*Corresponding author for this work

Department of Soil and Water Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove that Galilean invariant Schrödinger equations derived from Lagrangian densities necessarily obey the Ehrenfest theorem for velocity-independent potentials. The conclusion holds as well for Lagrangians describing nonlinear self-interactions. An example of Doebner and Goldin motivates the result.

Original language	English
Pages (from-to)	2999-3002
Number of pages	4
Journal	Journal of Physics A: Mathematical and General
Volume	37
Issue number	8
DOIs	https://doi.org/10.1088/0305-4470/37/8/011
State	Published - 27 Feb 2004

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abstract = "We prove that Galilean invariant Schr{\"o}dinger equations derived from Lagrangian densities necessarily obey the Ehrenfest theorem for velocity-independent potentials. The conclusion holds as well for Lagrangians describing nonlinear self-interactions. An example of Doebner and Goldin motivates the result.",

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AB - We prove that Galilean invariant Schrödinger equations derived from Lagrangian densities necessarily obey the Ehrenfest theorem for velocity-independent potentials. The conclusion holds as well for Lagrangians describing nonlinear self-interactions. An example of Doebner and Goldin motivates the result.

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Ehrenfest theorem, Galilean invariance and nonlinear Schrödinger equations

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