On the generalized unitary parasupersymmetry algebra of Beckers-Debergh

An appropriate generalization of the unitary parasupersymmetry algebra of Beckers-Debergh to arbitrary order is presented in this paper. A special representation for realizing of the even arbitrary order unitary parasupersymmetry algebra of Beckers-Debergh is analyzed by one dimensional shape invariance solvable models, 2D and 3D quantum solvable models obtained from the shape invariance theory as well. In particular in the special representation, it is shown that the isospectrum Hamiltonians consist of the two partner Hamiltonians of the shape invariance theory.