Extended supersymmetries for the Schrodinger-Pauli equation

It is argued that extended, reducible, and generalized supersymmetry (SUSY) are common in many systems of standard nonrelativistic quantum mechanics. For example, it is proved that a well-studied quantum mechanical system of a spin-1/2 particle interacting with constant and homogeneous magnetic fiel d admits the N = 4 SUSY and has the internal symmetry so(3,3). Then an appr oach of energy spectra of a SUSY nature is presented and developed. It is a pplied to a wide class of systems described by the Schrodinger-Pauli equati on admitting N = 3, N = 4, and N = 5 SUSY. Some of these supersymmetries ha ve a very peculiar property-their supercharges are realized without usual f ermionic variables. It is shown that for them, the usual extension N = 3 to N = 4 SUSY is no longer guaranteed. (C) 1999 American Institute of Physics . [S0022-2488(99)00203-0].