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Full-Text Articles in Physical Sciences and Mathematics
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Using supersymmetric quantum mechanics, one can obtain analytic expressions for the eigenvalues and eigenfunctions for all nonrelativistic shape invariant Hamiltonians. These Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent, group theoretical method. In this paper, we demonstrate the equivalence of the two methods of solution, and review related progress in this field.
Algebraic Shape Invariant Models, S Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya, Prasanta K. Panigrahi, C. Rasinariu, Uday P. Sukhatme
Algebraic Shape Invariant Models, S Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya, Prasanta K. Panigrahi, C. Rasinariu, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends previous results showing the equivalence of shape invariant potentials involving translational change of parameters with standard SO (2,1) potential algebra for Natanzon type potentials.