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Green’s Function of a General PT-Symmetric Non-Hermitian Non-central Potential

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Non-Hermitian Hamiltonians in Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 184))

Abstract

We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamiltonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green’s functions for a general non-central PT symmetric non hermitian potential are calculated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time.

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Acknowledgments

BPM acknowledge the financial support from the Department of Science and Technology (DST), Govt. of India under SERC project sanction grant No. SR/S2/HEP-0009/2012.

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Authors and Affiliations

  1. Department of Physics, Banaras Hindu University, Varanasi, 221005, India

    Brijesh Kumar Mourya & Bhabani Prasad Mandal

Authors
  1. Brijesh Kumar Mourya
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  2. Bhabani Prasad Mandal
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Correspondence to Bhabani Prasad Mandal .

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Editors and Affiliations

  1. Dipartimento di Energia, Università degli Studi di Palermo, Palermo, Italy

    Fabio Bagarello

  2. Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, Palermo, Palermo, Italy

    Roberto Passante

  3. Matematica e Informatica, Università degli Studi di Palermo, Palermo, Italy

    Camillo Trapani

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Mourya, B.K., Mandal, B.P. (2016). Green’s Function of a General PT-Symmetric Non-Hermitian Non-central Potential. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_21

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