New Two-Dimensional Quantum Models with Shape Invariance

Abstract

Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional SUSY Quantum Mechanics. They are obtained using the expressions for known one-dimensional shape invariant potentials. The constructed Hamiltonians are integrable with symmetry operators of fourth order in momenta, and they are not amenable to the conventional separation of variables.

16 p.p., a few new references added

References in corpus (3)

• Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation
• A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models

Cited by in corpus (7)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Analytical Solution of Two-Dimensional Scarf II Model by Means of SUSY Methods
• Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• General Solution of the Two-Dimensional Intertwining Relations for Supercharges with Hyperbolic (Lorentz) Metrics
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model