Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

Loading...
Thumbnail Image

Authors

Zander, Claudia
Plastino, Angel Ricardo (Angelo)
Diaz-Alonso, J.

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

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 timedependent solutions while previous studies focused on a stationary one.Weobtain 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 theNMequation, taking into account the fact that the evolution equation for the probability density ρ = |ψ|2 is not a continuity equation.Weshow 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.

Description

Keywords

Quantum measurement, Nonlinear Schrödinger equation, Nonlinear physics

Sustainable Development Goals

Citation

Zander, C, Plastino, AR & Díaz-Alonso, J 2015, 'Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements', Annals of Physics, vol. 362, pp. 36-56.