Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties

Details Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties

1999-02-16

arxiv.org/abs/quant-ph/9902057v2

Phys.Lett. A266 (2000) 341-349

Physics

Quantum Physics

18 pages, LaTeX, editorial page is removed

Scientific paper

10.1016/S0375-9601(00)00031-1

We study a complex intertwining relation of second order for Schroedinger operators and construct third order symmetry operators for them. A modification of this approach leads to a higher order shape invariance. We analyze with particular attention irreducible second order Darboux transformations which together with the first order act as building blocks. For the third order shape-invariance irreducible Darboux transformations entail only one sequence of equidistant levels while for the reducible case the structure consists of up to three infinite sequences of equidistant levels and, in some cases, singlets or doublets of isolated levels.

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