Relationship between supersymmetry and solvable potentials

Cooper, Fred ; Ginocchio, Joseph N. ; Khare, Avinash (1987) Relationship between supersymmetry and solvable potentials Physical Review D - Particles, Fields, Gravitation and Cosmology, 36 (8). pp. 2458-2473. ISSN 1550-7998

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We investigate whether a general class of solvable potentials, the Natanzon potentials (those potentials whose solutions are hypergeometric functions), and their supersymmetric partner potentials are related by a discrete reparametrization invariance called "shape invariance" discovered by Genden-shtein. We present evidence that this is not the case in general. Instead we find that the Natanzon class of potentials is not the most general class of solvable potentials but instead belongs to a wider class of potentials generated by supersymmetry and factorization whose eigenfunctions are sums of hypergeometric functions. The series of Hamiltonians, together with the corresponding supersymmetric charges form the graded Lie algebra sl(1/1)⊗SU(2). We also present a strategy for solving, in a limited domain, the discrete reparametrization invariance equations connected with "shape invariance".

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:82087
Deposited On:09 Feb 2012 09:51
Last Modified:09 Feb 2012 09:51

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