Artículo
Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
Fecha de publicación:
11/2015
Editorial:
Academic Press Inc Elsevier Science
Revista:
Annals of Physics (New York)
ISSN:
0003-4916
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ=|ψ|2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.
Palabras clave:
NONLINEAR PHYSICS
,
NONLINEAR SCHRÖDINGER EQUATION
,
QUANTUM MEASUREMENT
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Identificadores
Colecciones
Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Zander, C.; Plastino, Ángel Ricardo; Díaz Alonso, J.; Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements; Academic Press Inc Elsevier Science; Annals of Physics (New York); 362; 11-2015; 36-56
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