IJPAM: Volume 97, No. 1 (2014)
SUPERSYMMETRY ALGEBRA AND GROUP




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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This work is licensed under the Creative Commons Attribution International License (CC BY).