In this paper we discuss interacting particles in an external magnetic field. By comparing the Schr¨odinger equation of three interacting particles with the associated Laguerre differential equation, we obtain the energy spectrum which corresponds to indices ni and mi. 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
