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

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.

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

Published

August 2009