The method of intertwining with n-dimensional linear intertwining operator is used to construct isospectral, stationary potentials. It has been proven that the differential part of 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 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 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.
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August 2001
Research Article|
August 01 2001
Intertwined isospectral potentials in an arbitrary dimension
Ş. Kuru;
Ş. Kuru
Department of Physics, Ankara University, Faculty of Sciences, 06100, Tandoğan-Ankara, Turkey
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A. Teğmen;
A. Teğmen
Department of Physics, Ankara University, Faculty of Sciences, 06100, Tandoğan-Ankara, Turkey
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A. Verçin
A. Verçin
Department of Physics, Ankara University, Faculty of Sciences, 06100, Tandoğan-Ankara, Turkey
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J. Math. Phys. 42, 3344–3360 (2001)
Article history
Received:
March 05 2001
Accepted:
May 08 2001
Citation
Ş. Kuru, A. Teğmen, A. Verçin; Intertwined isospectral potentials in an arbitrary dimension. J. Math. Phys. 1 August 2001; 42 (8): 3344–3360. https://doi.org/10.1063/1.1383787
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