Algebraic Nature of Shape-Invariant and Self-Similar Potentials

Abstract

Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the latter can be generalized to the former. The infinite Lie algebras introduced in this context are shown to be closely related to the q-algebras. The associated coherent states are investigated.

8 pages

References in corpus (2)

• Algebraic Approach to Shape Invariance
• Algebraic Shape Invariant Models

Cited by in corpus (18)

• A Generalized Jaynes-Cummings Hamiltonian and Supersymmetric Shape-Invariance
• An Algebraic Construction of Generalized Coherent States for Shape-Invariant Potentials
• Barut-Girardello coherent states for nonlinear oscillator with position-dependent mass
• Completeness of Coherent States Associated with Self-Similar Potentials and Ramanujan's Integral Extension of the Beta Function
• Inter-relations between additive shape invariant superpotentials
• An Algebraic q-Deformed Form for Shape-Invariant Systems
• Coherent state of a nonlinear oscillator and its revival dynamics
• Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems
• Barrier Penetration for Supersymmetric Shape-Invariant Potentials
• Generalized Ladder Operators for the Dirac-Coulomb Problem via SUSY QM
• Coherent state of the effective mass harmonic oscillator
• Algebraic approach for shape invariant potentials in Klein-Gordon equation
• Ladder operators for subtle hidden shape invariant potentials
• Exactness of Semiclassical Quantization Rule for Broken Supersymmetry
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• A Relation Between $Z_3$-Graded Symmetry and Shape Invariant Supersymmetric Systems
• Algebraic Shape Invariant Potentials as the Generalized Deformed Oscillator
• Generalized Langer Correction and the Exactness of WKB for all Conventional Potentials