Bohmian Trajectories of Interacting Particles Trapped in a Two-dimensional Harmonic Well

Search for this publication on Google Scholar
Keithly, G. (2021). Bohmian Trajectories of Interacting Particles Trapped in a Two-dimensional Harmonic Well. Unc Charlotte Electronic Theses And Dissertations.
Download PDF

Analytics

38 views ◎
24 downloads ⇓


Abstract

Bohmian mechanics is an alternate formalism of quantum mechanics that posits a particle is always existent, and furthermore there is a separate entity describing a wave-like disturbance in space and time, governed by the Schrodinger equation, that affects the motion of particles through a quantum potential energy. While conceptually palatable, in applications Bohmian mechanics presents notable problems of stability and feasibility when it comes to numerical modeling of multiple particles. After demonstrating basic properties of a Bohmian trajectory for a single particle from an exact model, the approximation scheme developed by Oriols and co-workers is generalized and implemented for two and three particles in a two-dimensional harmonic confining potential well. The original approximation scheme involves a set of coupled Schrodinger equations, one per particle associated with a conditional wavefunction. This separation approach tremendously reduces the computational complexity. Unlike mean field theory typically used in multiple particle systems, the lowest level of this approximation scheme retains space-time correlations between particle motions. Here, this separation approach is extended to generalized coordinates. Consequently, particle dynamics is described by a set of separate conditional wavefunctions, where each conditional wavefunction is associated with a generalized coordinate and its non-commuting conjugate momentum. Correlations in time and space are calculated through a set of p coupled one-dimensional Schrodinger equations for p degrees of freedom in the system. Bohmian trajectories are feasibly calculated with far more practicality as demonstrated with two and three interacting particles.

Details
Author

Keithly, Gregory

Title

Bohmian Trajectories of Interacting Particles Trapped in a Two-dimensional Harmonic Well

Physical Description

1 online resource (40 pages) : PDF

Date

2021

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

Bohmian mechanics is an alternate formalism of quantum mechanics that posits a particle is always existent, and furthermore there is a separate entity describing a wave-like disturbance in space and time, governed by the Schrodinger equation, that affects the motion of particles through a quantum potential energy. While conceptually palatable, in applications Bohmian mechanics presents notable problems of stability and feasibility when it comes to numerical modeling of multiple particles. After demonstrating basic properties of a Bohmian trajectory for a single particle from an exact model, the approximation scheme developed by Oriols and co-workers is generalized and implemented for two and three particles in a two-dimensional harmonic confining potential well. The original approximation scheme involves a set of coupled Schrodinger equations, one per particle associated with a conditional wavefunction. This separation approach tremendously reduces the computational complexity. Unlike mean field theory typically used in multiple particle systems, the lowest level of this approximation scheme retains space-time correlations between particle motions. Here, this separation approach is extended to generalized coordinates. Consequently, particle dynamics is described by a set of separate conditional wavefunctions, where each conditional wavefunction is associated with a generalized coordinate and its non-commuting conjugate momentum. Correlations in time and space are calculated through a set of p coupled one-dimensional Schrodinger equations for p degrees of freedom in the system. Bohmian trajectories are feasibly calculated with far more practicality as demonstrated with two and three interacting particles.

Genre

masters theses

Subjects--Topics

Physics

Degree

M.S.

Keywords

Bohm
Bohmian
Model
Quantum

Subject Area

Applied Physics

Advisor(s)

Jacobs, Donald

Committee Members

Nesmelov, Yuri
Gbur, Greg

Degree Note

Thesis (M.S.)--University of North Carolina at Charlotte, 2021.

Rights Statement

This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). For additional information, see http://rightsstatements.org/page/InC/1.0/.

Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Keithly_uncc_0694N_13009

Permalink

http://hdl.handle.net/20.500.13093/etd:2817