The partnership of potentials in Quantum Mechanics and Shape Invariance

Abstract

The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate new factorizations from old ones using invariance under parameter transformations. The theory is illustrated with some examples.

10 pages, LaTeX, to appear in Modern Physics Letters A

References in corpus (6)

• A family of complex potentials with real spectrum
• Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties
• New hydrogen-like potentials
• The supersymmetric modified Poschl-Teller and delta-well potentials
• Integrability of Riccati equation from a group theoretical viewpoint
• Shape Invariant potentials depending on n parameters transformed by translation

Cited by in corpus (6)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Second order SUSY transformations with `complex energies'
• Trends in supersymmetric quantum mechanics
• On the new translational shape invariant potentials
• On the generalized unitary parasupersymmetry algebra of Beckers-Debergh
• Exactness of Semiclassical Quantization Rule for Broken Supersymmetry