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Non-Hermitian noncommutative quantum mechanics

  • J. F. G. dos SantosEmail author
  • F. S. Luiz
  • O. S. Duarte
  • M. H. Y. Moussa
Regular Article
  • 8 Downloads

Abstract.

In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilbert space structures, namely, those describing the non-Hermitian and noncommutative, Hermitian and noncommutative, and Hermitian and commutative systems. A general recipe is provided to obtain the expected values of the more general Hamiltonian. Finally, we apply our method to the harmonic oscillator under linear amplification and discuss the implications of both non-Hermitian and noncommutative effects.

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Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • J. F. G. dos Santos
    • 1
    Email author
  • F. S. Luiz
    • 2
  • O. S. Duarte
    • 2
  • M. H. Y. Moussa
    • 2
  1. 1.Universidade Federal do ABCSanto AndréBrazil
  2. 2.Instituto de Física de São CarlosUniversidade de São PauloSão CarlosBrazil

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