The Phase–Space Approach to time Evolution of Quantum States in Confined Systems: the Spectral Split

The Phase–Space Approach to time Evolution of Quantum States in Confined Systems: the Spectral Split–Operator Method

Published:2019-09-01 Issue:3 Volume:29 Page:439-451
ISSN:2083-8492
Container-title:International Journal of Applied Mathematics and Computer Science
language:en
Short-container-title:

Author:

Kołaczek Damian¹,Spisak Bartłomiej J.¹,Wołoszyn Maciej¹

Affiliation:

1. Faculty of Physics and Applied Computer Science , AGH University of Science and Technology , al. Mickiewicza 30, 30-059 Cracow , Poland

Abstract

Abstract Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.sciendo.com/pdf/10.2478/amcs-2019-0032

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