General forms of a N-fold supersymmetric family

We report general forms of one family of the N-fold supersymmetry in one-dimensional quantum mechanics. The N-fold supersymmetry is characterized by the supercharges which are Nth order in differential operators. The family reported here is defined as a particular form of the supercharges and is referred to as “type A”. We show that a quartic and a periodic potentials, which were previously found to be N-fold supersymmetric by the authors, are realized as special cases of this type A family.