Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
arXiv:0902.1837 · doi:10.1063/1.3133945
Abstract
The general solution of SUSY intertwining relations for three-dimensional Schrödinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary parameters. We are interested only in quantum systems which are not amenable to separation of variables, i.e. can not be reduced to lower dimensional problems. All constructed Hamiltonians are partially integrable - each of them commutes with a symmetry operator of fourth order in momenta. The same models can be considered also for complex values of parameters leading to a class of non-Hermitian isospectral Hamiltonians.
14 pages
References in corpus (22)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Supersymmetry and Quantum Mechanics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Higher-Derivative Supersymmetry and the Witten Index
- SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
- Second Order Derivative Supersymmetry and Scattering Problem
- Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
- New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance
- Intertwined isospectral potentials in an arbitrary dimension
- Matrix Hamiltonians: SUSY approach to hidden symmetries
- SUSY-Approach for Investigation of Two-Dimensional Quantum Mechanical Systems
- Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
- Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
- Chains of Darboux transformations for the matrix Schroedinger equation
- Intertwining relations of non-stationary Schrödinger operators
- New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
- Exact Solvability of Two-Dimensional Real Singular Morse Potential
- New Two-Dimensional Integrable Quantum Models from SUSY Intertwining
- Double Shape Invariance of Two-Dimensional Singular Morse Model
- Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
- Supersymmetric Construction of three-dimensional isospectral systems