New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables

Abstract

The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional generalization of well known one-dimensional Pöschl-Teller model is proven to be exactly solvable for arbitrary integer value of parameter $p:$ all its bound state energy eigenvalues are found analytically, and the algorithm for analytical calculation of all wave functions is given. The shape invariance of the model and its integrability are of essential importance to obtain these results.

23 pages

References in corpus (16)

• Supersymmetry and Quantum Mechanics
• Second Order Derivative Supersymmetry and Scattering Problem
• Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
• Intertwining technique for the one-dimensional stationary Dirac equation
• Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties
• New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance
• SUSY-Approach for Investigation of Two-Dimensional Quantum Mechanical Systems
• Connection Conditions and the Spectral Family under Singular Potentials
• SUSY Intertwining Relations of Third Order in Derivatives
• Self-adjoint extensions and spectral analysis in Calogero problem
• 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
• A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
• Double Shape Invariance of Two-Dimensional Singular Morse Model
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models

Cited by in corpus (9)

• 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
• General Solution of the Two-Dimensional Intertwining Relations for Supercharges with Hyperbolic (Lorentz) Metrics
• New Implicitly Solvable Potential Produced by Second Order Shape Invariance
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Infinite dimensional representations of cubic and quintic algebras and special functions
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane