相关论文: Energy Ambiguity in Nonlinear Quantum Mechanics
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
A Lagrangian description is presented which can be used in conjunction with particle interpretations of quantum mechanics. A special example of such an interpretation is the well-known Bohm model. The Lagrangian density introduced here also…
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant…
After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both…
It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
In the present contribution we consider a class of Schroedinger equations containing complex nonlinearities, describing systems with conserved norm $|\psi|^2$ and minimally coupled to an abelian gauge field. We introduce a nonlinear…
This paper is motivated by a gauged Schr\"odinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem: $$ - \Delta u(x) + \left(\omega +…
General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.
Three objections to the canonical analytical treatment of covariant electromagnetic theory are presented: (i) only half of Maxwell's equations are present upon variation of the fundamental Lagrangian; (ii) the trace of the canonical…
We establish the existence of a nontrivial weak solution to strongly indefinite asymptotically linear and superlinear Schr\"odinger equations. The novelty is to identify the essential relation between the spectrum of the operator and the…
In classical physics there is a well-known theorem in which it is established that the energy per degree of freedom is the same. However, in quantum mechanics due to the non-commutativity of some pairs of observables and the possibility of…
A new realization of the matter Lagrangian is introduced which models the dark energy component as a non-standard combination of thermodynamics quantities of the baryonic matter. We will prove that the present realization is independent of…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator…
The idea of equivalence of the free electromagnetic phase and quantum-mechanical one is investigated in an attempt to seek modifications of Schr\"{o}dinger's equation that could realize it. It is assumed that physically valid realizations…
Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\cal Q}_{\psi}^{\lambda}$, which presents a natural $C^{\infty}$ deformation of quantization, we obtain a uniquely selected non--linear, integro--differential…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…