Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability

Abstract

Recently, a new quantum model - two-dimensional generalization of the Scarf II - was completely solved analytically by SUSY method for the integer values of parameter. Now, the same integrable model, but with arbitrary values of parameter, will be studied by means of supersymmetrical intertwining relations. The Hamiltonian does not allow the conventional separation of variables, but the supercharge operator does allow, leading to the partial solvability of the model. This approach, which can be called as the first variant of SUSY-separation, together with shape invariance of the model, provides analytical calculation of the part of spectrum and corresponding wave functions (quasi-exact-solvability). The model is shown to obey two different variants of shape invariance which can be combined effectively in construction of energy levels and wave functions.

6 p.p., accepted for publication in EPL

References in corpus (6)

• 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
• Method for Generating Additive Shape Invariant Potentials from an Euler Equation
• New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
• New Two-Dimensional Quantum Models with Shape Invariance
• Analytical Solution of Two-Dimensional Scarf II Model by Means of SUSY Methods

Cited by in corpus (7)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• General Solution of the Two-Dimensional Intertwining Relations for Supercharges with Hyperbolic (Lorentz) Metrics
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• New Implicitly Solvable Potential Produced by Second Order Shape Invariance
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane