Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model

Abstract

We study a two-dimensional exactly solvable non-Hermitian $PT-$non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of pseudo-Hermiticity, biorthogonal expansion and pseudo-metric operator. To our knowledge this is the first time that pseudo-Hermiticity is realized explicitly for a nontrivial two-dimensional case. It is shown that the Hamiltonian of the model is not diagonalizable.

14 pages

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Cited by in corpus (10)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Exact Solvability of Two-Dimensional Real Singular Morse Potential
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• Pseudo supersymmetric partners for the generalized Swanson model
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• The Quantum Effective Mass Hamilton-Jacobi Problem
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Double complex SUSY-transformations: deformations of real potentials and their spectral characteristics