The confluent algorithm in second order supersymmetric quantum mechanics

Abstract

The confluent algorithm, a degenerate case of the second order supersymmetric quantum mechanics, is studied. It is shown that the transformation function must asymptotically vanish to induce non-singular final potentials. The technique can be used to create a single level above the initial ground state energy. The method is applied to the free particle, one-soliton well and harmonic oscillator.

arXiv comment9 pages, latex, 2 postscript figures

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• Wronskian formula for confluent second-order supersymmetric quantum mechanics
• Factorization method and new potentials from the inverted oscillator
• Supersymmetric partners of the trigonometric Poschl-Teller potentials
• Trends in supersymmetric quantum mechanics
• Wronskian differential formula for confluent supersymmetric quantum mechanics
• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
• On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
• Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
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• Wronskian differential formula for k-confluent SUSY QM
• The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
• Isospectral Potentials from Modified Factorization
• Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
• Bilayer graphene in magnetic fields generated by supersymmetry
• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• The generalized zero-mode supersymmetry scheme and the confluent algorithm
• Hyperconfluent third-order supersymmetric quantum mechanics
• Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design
• Nonlinear supersymmetry: from classical to quantum mechanics
• Ladder operators for the Ben Daniel-Duke Hamiltonians and their SUSY partners
• Nonsingular potentials from excited state factorization of a quantum system with position dependent mass
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Polynomial Supersymmetry for Matrix Hamiltonians
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Second-order Supersymmetric Operators and Excited States
• Infinite square-well, trigonometric Pöschl-Teller and other potential wells with a moving barrier
• Supersymmetry Transformations for Delta Potentials
• An affine Weyl group characterization of polynomial Heisenberg algebras
• Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• Polynomial supersymmetry for matrix Hamiltonians: proofs
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions
• Freezable bound states in the continuum for time-dependent quantum potentials