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Spatial confinement, non-Hermitian Hamiltonians and related problems

  • Regular Article - Atomic Physics
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Abstract

We treat simple examples of systems described by non-relativistic model Hamiltonians which are unconventional. They are not necessarily Hermitian operators. In practice, they often contain applied external fields which are not necessarily small, and they seek to describe the effects of spatial confinement more realistically than most of the classic calculations (some of them by the present authors). A much studied model of a free particle confined by a non-real potential can be accommodated within the same theoretical framework. Numerical treatment of these and similar problems seems well within the capacity of very modest computer systems, as exemplified by a few tabulations.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All calculated results are presented within the paper.]

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Acknowledgements

We wish to place on record our thanks to reviewers, whose helpful comments have led to a greatly improved version of the submitted work.

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Authors and Affiliations

  1. Mathematics Section School of Digital Technologies and Arts, Staffordshire University, College Road, Stoke-on-Trent, ST4 2DE, UK

    Brian L Burrows

  2. Department of Physical Chemistry, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Maurice Cohen

Authors
  1. Brian L Burrows
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  2. Maurice Cohen
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Correspondence to Brian L Burrows.

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Burrows, B.L., Cohen, M. Spatial confinement, non-Hermitian Hamiltonians and related problems. Eur. Phys. J. D 75, 70 (2021). https://doi.org/10.1140/epjd/s10053-021-00093-9

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  • DOI: https://doi.org/10.1140/epjd/s10053-021-00093-9

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