Two-dimensional SUSY-pseudo-Hermiticity without separation of variables

Abstract

We study SUSY-intertwining for non-Hermitian Hamiltonians with special emphasis to the two-dimensional generalized Morse potential, which does not allow for separation of variables. The complexified methods of SUSY-separation of variables and two-dimensional shape invariance are used to construct particular solutions - both for complex conjugated energy pairs and for non-paired complex energies.

14 pages, Latex

References in corpus (22)

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Cited by in corpus (23)

• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
• Bloch-like waves in random-walk potentials based on supersymmetry
• Spectra of PT-Symmetric Operators and Perturbation Theory
• SUSY-Approach for Investigation of Two-Dimensional Quantum Mechanical Systems
• New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• New Two-Dimensional Integrable Quantum Models from SUSY Intertwining
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Double Shape Invariance of Two-Dimensional Singular Morse Model
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Quadratic pseudosupersymmetry in two-level systems
• On two-dimensional superpotentials: from classical Hamilton-Jacobi theory to 2D supersymmetric quantum mechanics
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
• Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
• Canonical Expansion of PT-Symmetric Operators and Perturbation Theory
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum