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

N. Aizawa·H. -T. Sato
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Abstract

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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N. Aizawa, H. -T. Sato. 1997-08-06. Isospectral Hamiltonians and $W_{1+\infty}$ algebra. https://doi.org/10.1143/ptp.98.707

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