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    • Solution of an analogous Schrödinger equation for $\mathcal{PT}$-symmetric sextic potential in two dimensions

      Fakir Chand S C Mishra Ram Mehar Singh

      Volume 73 Issue 2 August 2009 pp 349-361

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      https://www.ias.ac.in/article/fulltext/pram/073/02/0349-0361

    • Keywords

       

      Schrödinger equation; complex Hamiltonian; $\mathcal{PT}$ symmetry; eigenvalues and eigenfunctions.

    • Abstract

       

      We investigate the quasi-exact solutions of an analogous Schrödinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}$, $y = x_{2} + ip_{4}$, $p_{x} = p_{1} + ix_{3}$, $p_{y} = p_{2} + ix_{4}$. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional $\mathcal{PT}$-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.

    • Author Affiliations

       

      Fakir Chand1 S C Mishra1 Ram Mehar Singh2

      1. Department of Physics, Kurukshetra University, Kurukshetra 136 119, India
      2. Department of Physics, Ch. Devi Lal University, Sirsa 125 055, India

    • Dates

       
      Published
      August 2009

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