Exactly solvable models of supersymmetric quantum mechanics and connection to spectrum generating algebra

Details Exactly solvable models of supersymmetric quantum mechanics and connection to spectrum generating algebra Exactly solvable models of supersymmetric quantum mechanics and connection to spectrum generating algebra

1998-10-12

arxiv.org/abs/hep-th/9810074v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 2 figures

Scientific paper

10.1007/BF02557323

For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent group theoretic method. In this paper, we demonstrate the equivalence of the two methods of solution by developing an algebraic framework for shape invariant Hamiltonians with a general change of parameters, which involves nonlinear extensions of Lie algebras.

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