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

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Book cover Information Technology, Systems Research, and Computational Physics (ITSRCP 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((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.

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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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Authors and Affiliations

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

    Damian Kołaczek, Bartłomiej J. Spisak & Maciej Wołoszyn

Authors
  1. Damian Kołaczek
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  2. Bartłomiej J. Spisak
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  3. Maciej Wołoszyn
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Corresponding author

Correspondence to Bartłomiej J. Spisak .

Editor information

Editors and Affiliations

  1. Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

    Piotr Kulczycki

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  3. Faculty of Engineering Sciences, Széchenyi István University, Győr, Hungary

    László T. Kóczy

  4. Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  5. Department of Electronic Systems, Aalborg University, Aalborg, Denmark

    Rafal Wisniewski

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Kołaczek, D., Spisak, B.J., Wołoszyn, M. (2020). P\(\hbar \)ase-Space Approach to Time Evolution of Quantum States in Confined Systems. The Spectral Split-Operator Method. In: Kulczycki, P., Kacprzyk, J., Kóczy, L., Mesiar, R., Wisniewski, R. (eds) Information Technology, Systems Research, and Computational Physics. ITSRCP 2018. Advances in Intelligent Systems and Computing, vol 945. Springer, Cham. https://doi.org/10.1007/978-3-030-18058-4_24

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