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Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having \(\mathcal{PT}\)symmetry

  • B. F. Ramos
  • I. A. Pedrosa
  • Alberes Lopes de Lima
Regular Article

Abstract.

We discuss the extension of the Lewis and Riesenfeld invariant method to cases where the quantum systems are modulated by time-dependent non-Hermitian Hamiltonians having \(\mathcal{PT}\) symmetry. As an explicit example of this extension, we study the quantum motion of a particle submitted to action of a complex time-dependent linear potential with \(\mathcal{PT}\) symmetry. We solve the time-dependent Schrödinger equation for this problem and construct a Gaussian wave packet solution. Afterwards, we use this Gaussian packet to calculate the expectation values of the position and the momentum and the uncertainty product. We find that these expectation values are complex numbers and consequently the position and momentum operators are not observables.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • B. F. Ramos
    • 1
  • I. A. Pedrosa
    • 1
  • Alberes Lopes de Lima
    • 2
  1. 1.Departamento de Física, CCENUniversidade Federal da ParaíbaJoão PessoaBrazil
  2. 2.Colégio Militar do RecifeDepartamento de Ensino e Pesquisa do Exército BrasileiroRecifeBrazil

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