Isospectral Hamiltonians and $W_{1+\infty}$ algebra

Details Isospectral Hamiltonians and $W_{1+\infty}$ algebra Isospectral Hamiltonians and $W_{1+\infty}$ algebra

1996-01-26

arxiv.org/abs/quant-ph/9601026v2

Prog.Theor.Phys. 98 (1997) 707-718

Physics

Quantum Physics

15 pages, LaTeX, one postscript figure available by request version appearing in Prog. Theore. Phys

Scientific paper

10.1143/PTP.98.707

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 $W_{1+\infty}$ 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.

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