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P\(\hbar \)ase-Space Approach to Time Evolution of Quantum States in Confined Systems. The Spectral Split-Operator Method

  • Damian Kołaczek
  • Bartłomiej J. SpisakEmail author
  • Maciej Wołoszyn
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 945)

Abstract

Using the phase space approach, we consider the dynamics of a quantum particle in an isolated confined quantum 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 used algorithm by analysis of the total energy expectation value, in terms of the deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

Keywords

Wigner distribution function Moyal dynamics Split-operator method 

Notes

Acknowledgement

This work was partially supported by the Faculty of Physics and Applied Computer Science AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education. D.K. has been partly supported by the EU Project POWR.03.02.00-00-I004/16.

The preliminary version of this paper was presented at the 3rd Conference on Information Technology, Systems Research and Computational Physics, 2–5 July 2018, Cracow, Poland [37].

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Damian Kołaczek
    • 1
  • Bartłomiej J. Spisak
    • 1
    Email author
  • Maciej Wołoszyn
    • 1
  1. 1.Faculty of Physics and Applied Computer ScienceAGH University of Science and TechnologyKrakówPoland

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