Second-order Supersymmetric Operators and Excited States

Abstract

Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate that the existence of raising and lowering operators for the harmonic oscillator (and many other potentials) can be extended to their supersymmetric partners. The use of double supersymmetry (or a factorization chain) is used to obtain non-singular isospectral potentials, and the explicit expressions for the ladder operators, wave functions and probability densities are provided. This application avoids the technical complexities of the most general approaches, and requires relatively modest methods from supersymmetric quantum mechanics.

8 pages, 3 figures

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• Supersymmetry and Quantum Mechanics
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Cited by in corpus (6)

• Isospectral Potentials from Modified Factorization
• Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
• Hyperconfluent third-order supersymmetric quantum mechanics
• 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
• Singular Isotonic Oscillator, Supersymmetry and Superintegrability