IJPAM: Volume 97, No. 1 (2014)

BRIEFLY REVISITING THE QUANTUM MECHANICS
SUPERSYMMETRY ALGEBRA AND GROUP

R. Thibes$^1$, E.F. Batista$^2$, G.D. Barbosa$^3$
$^{1,2,3}$Departamento de Ciências Exatas e Naturais
Universidade Estadual do Sudoeste da Bahia
Itapetinga, BA, BRASIL


Abstract. We review supersymmetry (SUSY) in nonrelativistic quantum mechanics emphasizing algebraic aspects. We discuss the Hamiltonian subgroup implementing supersymmetry as well as the corresponding algebra of the SUSY generators. In the SUSYQM framework, the two distinct partner potentials are connected by a superpotential satisfying a Riccati differential equation. A full Hamiltonian operator in an extended Hilbert space is defined in order to render the supersymmetry manifest. As a result, the eigenfunctions of the original potentials are connected by generalized ladder operators. We provide an explicit realization of the abstract supersymmetry group for SUSYQM depending on one real and two Grassmann parameters.

Received: August 6, 2014

AMS Subject Classification: 08A99, 17B81, 81R15

Key Words and Phrases: supersymmetry, supersymmetric quantum mechanics, factorization method, supergroups, superalgebra

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DOI: 10.12732/ijpam.v97i1.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 1
Pages: 99 - 109


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