Spectrum-generating symmetries for the Superpotentials \(A\) cot \(\theta \) and \(B\) tanh \(y\)

DOI10.1007/s10773-008-9699-9zbMath1157.81319OpenAlexW2078149422MaRDI QIDQ1008185

Hossein Fakhri

Publication date: 24 March 2009

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-008-9699-9

zbMATH Keywords

ordinary differential equationsspecial functionssuperpotentialsfactorization methodsshape invariance symmetriessupersymmetry in quantum mechanics

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10)

Cites Work

• Unnamed Item
• Unnamed Item
• Dynamical breaking of supersymmetry
• Embedding of dynamical symmetry groups \(U(1,1)\) and \(U(2)\) of a free particle on AdS\(_2\) and \(S^2\) into parasupersymmetry algebra
• Ladder operators and recursion relations for the associated Bessel polynomials
• Alternative approach to the concept of shape invariance in quantum mechanics
• Systems with higher-order shape invariance: spectral and algebraic properties
• Shape invariance symmetries for quantum states of the superpotentials \(A\tanh\omega y+B/A\) and \(- A\cot\omega \theta +B\csc\omega \theta \)
• Ladder operators for the associated Laguerre functions
• Algebraic nature of shape-invariant and self-similar potentials
• Connection between type B (or C) and F factorizations and construction of algebras
• Intertwining relations for the matrix Calogero-like models: supersymmetry and shape invariance
• Shape invariance and laddering equations for the associated hypergeometric functions
• Shape invariant potentials withcalPcalTsymmetry
• Connection between type A and E factorizations and construction of satellite algebras
• Ladder operators for subtle hidden shape-invariant potentials
• The Factorization Method
• Broken supersymmetric shape invariant systems and their potential algebras