Abstract
Dynamical and kinematical symmetries and supersymmetries of the n-dimensional harmonic oscillator are discussed in connection with two different supersymmetrisation procedures: the so-called standard and spin-orbit coupling procedures. The largest invariance structures appear within the standard procedure dealing with the same numbers of bosonic and fermionic degrees of freedom. The authors also obtain meaningful substructures within the spin-orbit coupling procedure dealing with fermionic degrees of freedom which are half of the bosonic ones. Finally the n=2 case is connected with the study of the motion in a constant magnetic field. Each procedure leads to a nice correspondence between the two systems under consideration.
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