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Intertwined isospectral potentials in an arbitrary dimension
S. Kuru, A. Tegmen, A. Vercin
abstract: The method of intertwining with n-dimensional (nD) linear intertwining
operator L is used to construct nD isospectral, stationary potentials. It has
been proven that differential part of L is a series in Euclidean algebra
generators. Integrability conditions of the consistency equations are
investigated and the general form of a class of potentials respecting all these
conditions have been specified for each n=2,3,4,5. The most general forms of 2D
and 3D isospectral potentials are considered in detail and construction of
their hierarchies is exhibited. The followed approach provides coordinate
systems which make it possible to perform separation of variables and to apply
the known methods of supersymmetric quantum mechanics for 1D systems. It has
been shown that in choice of coordinates and L there are a number of
alternatives increasing with $n$ that enlarge the set of available potentials.
Some salient features of higher dimensional extension as well as some
applications of the results are presented.
- oai_identifier:
- oai:arXiv.org:quant-ph/0111034
- categories:
- quant-ph math-ph math.MP nlin.SI
- comments:
- 14 pages, Latex file
- doi:
- 10.1063/1.1383787
- arxiv_id:
- quant-ph/0111034
- journal_ref:
- J. Math. Phys. 42 (2001) 3344-3360
- created:
- 2001-11-06
Full article ▸
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