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Translational Shape Invariance And The Inherent Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatne
Translational Shape Invariance And The Inherent Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
For all quantum-mechanical potentials that are known to be exactly solvable, there are two different, and seemingly independent methods of solution. The first approach is the potential algebra of symmetry groups; the second is supersymmetric quantum mechanics, applied to shape-invariant potentials, which comprise the set of known exactly solvable potentials. Using the underlying algebraic structures of Natanzon potentials, of which the translational shape-invariant potentials are a special subset, we demonstrate the equivalence of the two methods of solution. In addition, we show that, while the algebra for the general Natanzon potential is so(2,2), the subgroup so(2,1) suffices for the shape …
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.
Shape Invariance And Its Connection To Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatme
Shape Invariance And Its Connection To Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority of these potentials have also been shown to possess a potential algebra, and hence are also solvable by group theoretical techniques. In this paper, for a subset of solvable problems, we establish a connection between the two methods and show that they are indeed equivalent.