Exact Solvability of Two-Dimensional Real Singular Morse Potential

Abstract

The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This two-parametric model is not amenable to conventional separation of variables, but it is completely integrable: the symmetry operator of fourth order in momenta exists. All bound state energies are found explicitly, and all corresponding wave functions are built analytically. By means of shape invariance property, the result is extended to the hierarchy of Morse models with arbitrary integer and half-integer values $a_k=-(k+1)/2.$

11 pages

References in corpus (6)

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• New Two-Dimensional Integrable Quantum Models from SUSY Intertwining
• Double Shape Invariance of Two-Dimensional Singular Morse Model
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• New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
• Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
• New Two-Dimensional Quantum Models with Shape Invariance
• Analytical Solution of Two-Dimensional Scarf II Model by Means of SUSY Methods
• Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation
• Two-dimensional Schrödinger Hamiltonians with Effective Mass in SUSY Approach
• Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
• New Implicitly Solvable Potential Produced by Second Order Shape Invariance
• Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
• Degeneracy and coherent states of the two-dimensional Morse potential
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• On the Supersymmetric Spectra of two Planar Integrable Quantum Systems
• Non-linear ladder operators and coherent states for the 2:1 oscillator
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
• Coherent states of the two-dimensional non-separable supersymmetric Morse potential