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An efficient method to solve the Schrödinger equation with complex PT-symmetric potentials

Author

Listed:
  • F.-Z. Rouabhi

    (Département de Physique, Faculté des Sciences, Université M’Hamed Bougara de Boumerdes, Avenue de l’indépendance, 35000 Boumerdes, Algeria†Laboratoire Revêtement Matériaux et Environnement LRME, Bloc de Recherche, Campus Nord, Université M’Hamed Bougara, de Boumerdes 35000, Algeria)

  • I. Ami

    (Département de Physique, Faculté des Sciences, Université M’Hamed Bougara de Boumerdes, Avenue de l’indépendance, 35000 Boumerdes, Algeria‡Laboratoire de Physique Théorique, Faculté de Physique, Université des Sciences Et de la Technologie Houari Boumediene, BP 32, El Alia 16111 Bab-Ezzouar, Algeria)

  • R. Mezhoud

    (Département de Physique, Faculté des Sciences, Université M’Hamed Bougara de Boumerdes, Avenue de l’indépendance, 35000 Boumerdes, Algeria†Laboratoire Revêtement Matériaux et Environnement LRME, Bloc de Recherche, Campus Nord, Université M’Hamed Bougara, de Boumerdes 35000, Algeria)

  • R. J. Lombard

    (IJClab, Orsay, F-91406 Orsay Cedex, France)

Abstract

In this work, we present a simple and efficient method to compute numerically the eigenvalues of complex PT-symmetric Hamiltonian. Numerous works have been devoted to such Hamiltonians since the discovery that they admit totally or partially real spectra. To our knowledge, the method we are advocating has not been used in this context. Besides the determination of real eigenvalues, it allows us to observe the symmetry breaking and to calculate the imaginary parts of the energy.

Suggested Citation

  • F.-Z. Rouabhi & I. Ami & R. Mezhoud & R. J. Lombard, 2023. "An efficient method to solve the Schrödinger equation with complex PT-symmetric potentials," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-10, May.
    • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:05:n:s0129183123500651
    DOI: 10.1142/S0129183123500651
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