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In this paper we discuss the interacting particles in an
external magnetic field. By comparing the Schr\"odinger equation of
three - interacting particles with associated Laguerre differential
equation, we obtain the energy spectrum which correspondes 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.
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