Generalized Ehrenfest Theorem for Nonlinear Schrodinger Equations

    loading  Checking for direct PDF access through Ovid

Abstract

It is shown that the Ehrenfest theorem can be generalized so that it is valid also for all space-localized solutions ψ of the nonlinear Schrödinger equations (in one or more space dimensions). Then it is shown that as a consequence, the motion of the localized ψ-field as a whole obeys the laws of classical mechanics and those of classical electrodynamics if the interaction of the ψ-field with an external electromagnetic field is defined by the rules of quantum mechanics applied to the nonlinear Schrödinger equation for ψ (in exactly the same manner as to the linear Schrödinger equation). This establishes the existence of a deep link between the nonlinear Schrödinger equations and classical mechanics and electrodynamics.

Related Topics

    loading  Loading Related Articles