POLYNOMIAL SUSY IN QUANTUM-MECHANICS AND 2ND DERIVATIVE DARBOUX TRANSFORMATIONS

We give a classification of second-order polynomial SUSY quantum mecha nics in one and two dimensions. Particular attention is paid to the ir reducible supercharges which cannot be built by repetition of ordinary Darboux transformations. In two dimensions it is found that the binom ial superalgebra leads to the dynamic symmetry generated by a central charge operator.