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- W1621360522 abstract "We observe that in nonlinear quantum mechanics, unlike in the linear theory, there exists, in general, a difference between the energy functional defined within the Lagrangian formulation as an appropriate conserved component of the canonical energy-momentum tensor and the energy functional defined as the expectation value of the corresponding nonlinear Hamiltonian operator. Some examples of such ambiguity are presented for a particularly simple model and some known modifications. However, we point out that there exist a class of nonlinear modifications of the Schr{o}dinger equation where this difference does not occur, which makes them more consistent in a manner similar to that of the linear Schr{o}dinger equation. It is found that necessary but not sufficient a condition for such modifications is the homogeneity of the modified Schr{o}dinger equation or its underlying Lagrangian density which is assumed to be ``bilinear'' in the wave function in some rather general sense. Yet, it is only for a particular form of this density that the ambiguity in question does not arise. A salient feature of this form is the presence of phase functionals. The present paper thus introduces a new class of modifications characterized by this desirable and rare property." @default.
- W1621360522 created "2016-06-24" @default.
- W1621360522 creator A5052260071 @default.
- W1621360522 date "1998-02-03" @default.
- W1621360522 modified "2023-09-27" @default.
- W1621360522 title "Energy Ambiguity in Nonlinear Quantum Mechanics" @default.
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