Isospectral Hamiltonians and W1+∞ algebra

We discuss a spectrum generating algebra in the supersymmetric quantum mechanical system which is defined as a series of solutions to a specific differential equation. All Hamiltonians have equally spaced eigenvalues, and we realize both positive and negative mode generators of a subalgebra of W1+∞ without use of negative power of raising/lowering operators of the system. All features in the supersymmetric case are generalized to the parasupersymmetric systems of order 2. ——————————————————————† Fellow of the Danish Research Academy E-mail : [email protected] ∗ E-mail : [email protected]