EXACT SOLUTIONS OF DIRAC AND SCHRÖDINGER EQUATIONS FOR A LARGE CLASS OF POWER-LAW POTENTIALS AT ZERO ENERGY

DOI10.1142/S0217751X02010911zbMath1016.81021arXivmath-ph/0112001MaRDI QIDQ4792859

A. D. Alhaidari

Publication date: 18 August 2003

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

Full work available at URL: https://arxiv.org/abs/math-ph/0112001

zbMATH Keywords

confluent hypergeometric functionspoint canonical transformationsexactly solvable problembound states at zero energyrepresentations of \(\text{SO}(2, 1)\) Lie algebra

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) PDEs in connection with quantum mechanics (35Q40) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

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Cites Work

• Dynamical breaking of supersymmetry
• General properties of potentials for which the Schrödinger equation can be solved by means of hypergeometric functions
• Quasi-exactly-solvable problems and sl(2) algebra
• Zero-energy states for a class of quasi-exactly solvable rational potentials.
• Elementary Theory of Resonance Scattering

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