Eur. Phys. J. B 50, 453-457 (2006)
https://doi.org/10.1140/epjb/e2006-00150-9

Superalgebras for three interacting particles in an external magnetic field

Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5531, Tehran, Iran and Department of Physics Faculty of Sciences, Mazandaran University, P.O. Box 47415, Babolsar, Iran

Corresponding author: ^a pouriya@ipm.ir

Received: 11 April 2005
Revised: 24 October 2005
Published online: 5 May 2006

Abstract

In this paper we discuss interacting particles in an external magnetic field. By comparing the Schrödinger equation of three interacting particles with the associated Laguerre differential equation, we obtain the energy spectrum which corresponds to indices n_i and m_i. Finally by using the so called factorization method we obtain the raising and lowering operators. These operators are supersymmetric structures related to the Hamiltonian partner. Also these operators lead to the realization of Heisenberg Lie superalgebras with two, four and six supercharges.