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Generalized Ehrenfest Theorem for Nonlinear Schrodinger Equations

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Abstract

It is shown that the Ehrenfest theorem can begeneralized so that it is valid also for allspace-localized solutions ψ of the nonlinearSchrodinger equations (in one or more space dimensions).Then it is shown that as a consequence, the motion ofthe localized ψ-field as a whole obeys the laws ofclassical mechanics and those of classicalelectrodynamics if the interaction of the ψ-fieldwith an external electromagnetic field is defined bythe rules of quantum mechanics applied to the nonlinearSchrodinger equation for ψ (in exactly the samemanner as to the linear Schrodinger equation). This establishes the existence of a deep linkbetween the nonlinear Schrodinger equations andclassical mechanics and electrodynamics.

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Authors
  1. T. G. Bodurov
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Bodurov, T.G. Generalized Ehrenfest Theorem for Nonlinear Schrodinger Equations. International Journal of Theoretical Physics 37, 1299–1306 (1998). https://doi.org/10.1023/A:1026632006040

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