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    • Level crossings in complex two-dimensional potentials

      Qing-Hai Wang

      Volume 73 Issue 2 August 2009 pp 315-322

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/073/02/0315-0322

    • Keywords

       

      Non-Hermitian; $\mathcal{PT}$ symmetry; two-dimensional potentials.

    • Abstract

       

      Two-dimensional $\mathcal{PT}$-symmetric quantum-mechanical systems with the complex cubic potential $V_{12} = x^{2} + y^{2} + igxy^{2}$ and the complex Hénon–Heiles potential $V_{\text{HH}} = x^{2} + y^{2} + ig(xy^{2} − x^{3}/3)$ are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $\mathcal{PT}$ symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.

    • Author Affiliations

       

      Qing-Hai Wang1

      1. Department of Physics, National University of Singapore, Singapore 117542

    • Dates

       
      Published
      August 2009

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