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Systems with higher order shape invariance: Spectral and algebraic properties

Alexander A. Andrianov
(
- Barcelona U.
)
,
F. Cannata
(
- Barcelona U.
)
,
Mikhail V. Ioffe
(
- Barcelona U.
)
,
D. Nishnianidze
(
- Barcelona U.
)

Feb, 1999

19 pages

Published in:

Phys.Lett.A 266 (2000) 341-349

e-Print:

quant-ph/9902057 [quant-ph]

DOI:

10.1016/S0375-9601(00)00031-1

View in:

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Abstract:

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.

Note:

18 pages, LaTeX, editorial page is removed

References(21)

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