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

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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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Authors and Affiliations

  1. Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900, João Pessoa, PB, Brazil

    B. F. Ramos & I. A. Pedrosa

  2. Colégio Militar do Recife, Departamento de Ensino e Pesquisa do Exército Brasileiro, 50721-420, Recife, PE, Brazil

    Alberes Lopes de Lima

Authors
  1. B. F. Ramos
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  2. I. A. Pedrosa
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  3. Alberes Lopes de Lima
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Correspondence to I. A. Pedrosa.

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Ramos, B.F., Pedrosa, I.A. & Lopes de Lima, A. Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having \(\mathcal{PT}\)symmetry. Eur. Phys. J. Plus 133, 449 (2018). https://doi.org/10.1140/epjp/i2018-12251-3

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  • DOI: https://doi.org/10.1140/epjp/i2018-12251-3

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