Shape invariant Natanzon potential hierarchy and its twin: a novel approach

DOI10.1016/j.physleta.2005.02.016zbMath1136.81354OpenAlexW2061198574MaRDI QIDQ2478782

A. Chenaghlou, Hossein Fakhri

Publication date: 25 March 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2005.02.016

zbMATH Keywords

ordinary differential equationsquantum mechanicssupersymmetryladder operatorsshape invariance

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Supersymmetry and quantum mechanics (81Q60)

Related Items (1)

Energy spectra of the hyperbolic and second Pöschl-Teller like potentials solved by new exact quantization rule

Cites Work

• Group theory approach to scattering
• General properties of potentials for which the Schrödinger equation can be solved by means of hypergeometric functions
• Relations between 1D shape invariant potentials and the commutation relations of the Lie algebra sl\((2,\mathbb{C})\)
• \(\mathcal{PT}\) symmetry of a conditionally exactly solvable potential
• 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
• A class of exactly solvable potentials related to the Jacobi polynomials
• The potential group approach and hypergeometric differential equations
• $\Script P$$\Script T$-symmetric potentials and the so(2, 2) algebra
• Shape invariance and laddering equations for the associated hypergeometric functions
• An exactly solvable    symmetric potential from the Natanzon class

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