Isospectral Potentials from Modified Factorization

Abstract

Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.

8 pages, 4 figures

References in corpus (5)

• A quantum exactly solvable non-linear oscillator related with the isotonic oscillator
• New hydrogen-like potentials
• The confluent algorithm in second order supersymmetric quantum mechanics
• Wronskian formula for confluent second-order supersymmetric quantum mechanics
• Second-order Supersymmetric Operators and Excited States

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• Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
• Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis
• Nonsingular potentials from excited state factorization of a quantum system with position dependent mass
• Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators
• Ladder operators and squeezed coherent states of a 3-dimensional generalized isotonic nonlinear oscillator
• A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator
• Singular Isotonic Oscillator, Supersymmetry and Superintegrability
• Revisiting an isospectral extension of the Morse potential