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QES solutions of a two-dimensional system with quadratic nonlinearities

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Abstract

We consider a one-parameter family of a PT symmetric two-dimensional system with quadratic nonlinearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this system by constructing a non-Hermitian Hamiltonian of a particle with position-dependent mass. We further construct a canonical transformation which maps this position-dependent mass system to a QES system. First few QES levels are calculated explicitly by using Bender–Dunne polynomial method.

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Notes

  1. In two dimension parity transformation can be defined in three alternative ways \((x,y)\rightarrow (x,-y),(x,y)\rightarrow (-x,y) \ \ \text{ and } (x,y)\rightarrow (y,x) \).

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Authors and Affiliations

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

    Bhabani Prasad Mandal, Brijesh Kumar Mourya & Aman Kumar Singh

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

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Mandal, B.P., Mourya, B.K. & Singh, A.K. QES solutions of a two-dimensional system with quadratic nonlinearities. Eur. Phys. J. Plus 135, 327 (2020). https://doi.org/10.1140/epjp/s13360-020-00335-6

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