Energy Ambiguity in Nonlinear Quantum Mechanics
| dc.creator | Puszkarz, Waldemar | |
| dc.date | 1998-02-03 | |
| dc.date | 1999-05-17 | |
| dc.date.accessioned | 2026-07-07T06:14:44Z | |
| dc.date.available | 2026-07-07T06:14:44Z | |
| dc.description | 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 Schrödinger equation where this difference does not occur, which makes them more consistent in a manner similar to that of the linear Schrödinger equation. It is found that necessary but not sufficient a condition for such modifications is the homogeneity of the modified Schrödinger 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. | |
| dc.description | Slightly extended, new references added, Latex, 15 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9802001 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9802001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/93577 | |
| dc.subject | Quantum Physics | |
| dc.title | Energy Ambiguity in Nonlinear Quantum Mechanics | |
| dc.type | text |