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

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.

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

References in corpus (1)

• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle

Cited by in corpus (5)

• Coherent states for Hamiltonians generated by supersymmetry
• Trends in supersymmetric quantum mechanics
• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
• Polynomial Heisenberg algebras, multiphoton coherent states and geometric phases
• Multiphoton supercoherent states