Zander, ClaudiaPlastino, Angel Ricardo (Angelo)Diaz-Alonso, J.2015-09-082015-09-082015-11Zander, 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. 36-56.0003-4916 (print)1096-035X (online)10.1016/j.aop.2015.07.019http://hdl.handle.net/2263/49740We 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.en© 2015 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Annals of Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Annals of Physics, vol. 262, pp. 36-56, 2015. doi : 10.1016/j.aop.2015.07.019.Quantum measurementNonlinear Schrödinger equationNonlinear physicsPostprint Article