The Multidimensional Darboux transformation
| dc.contributor.author | González López, Artemio | |
| dc.contributor.author | Kamran, Niky | |
| dc.date.accessioned | 2023-06-20T20:09:56Z | |
| dc.date.available | 2023-06-20T20:09:56Z | |
| dc.date.issued | 1998-07 | |
| dc.description | © Elsevier. One of the authors (A.G.-L.) would like to thank A. Galindo, M. Mañas and M. A. Martín Delgado for helpful conversations. | |
| dc.description.abstract | A generalization of the classical one-dimensional Darboux transformation to arbitrary n- dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of dimension n ≥ 2. New examples of quasi-exactly solvable multidimensional matrix Schrödinger operators on curved manifolds are obtained by applying the above results. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/32861 | |
| dc.identifier.doi | 10.1016/S0393-0440(97)00044-2 | |
| dc.identifier.issn | 0393-0440 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1016/S0393-0440(97)00044-2 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.relatedurl | http://arxiv.org/abs/hep-th/9612100 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59724 | |
| dc.issue.number | 3-abr. | |
| dc.journal.title | Journal of geometry and physics | |
| dc.language.iso | eng | |
| dc.page.final | 226 | |
| dc.page.initial | 202 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Quantum-systems | |
| dc.subject.keyword | Supersymmetry | |
| dc.subject.keyword | Dimensions | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | The Multidimensional Darboux transformation | |
| dc.type | journal article | |
| dc.volume.number | 26 | |
| dcterms.references | [1] Andrianov, A. A., Borissov, N. V., and Ioffe, M. V., The factorization method and quantum systems with equivalent energy spectra, Phys. Lett. 105A (1984), 19–22. [2] Andrianov, A. A., Borissov, N. V., Eides, M. I., and Ioffe, M. V., Supersymmetric origin of equivalent quantum systems, Phys. Lett. 109A (1985), 143–148. [3] Crum, M. M., Associated Sturm–Liouville equations, Q. J. Math. 6 (1955), 121–127. [4] Darboux, G., Théorie générale des surfaces, vol. II, Gauthier–Villars, Paris, 1888. [5] Deift, P., and Trubowitz, E., Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), 121– 251. [6] Goursat, E., Le¸cons sur l’ intégration des equations aux dérivées partielles du second ordre, Hermann, Paris, 1896. [7] González-López, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, Commun. Math. Phys. 159 (1994), 503–537. [8] González–López, A., Kamran, N., and Olver, P.J., Quasi–exact solvability, Contemp. Math. 160 (1994), 113–140. [9] González-López, A., Kamran, N., and Olver, P.J., Real Lie algebras of differential operators and quasi- exactly solvable potentials, Phil. Trans. London Math. Soc. A354 (1996), 1165–1193. [10] Infeld, L., and Hull, T., The factorization method, Revs. Mod. Phys. 23 (1951), 21–68. [11] Kamran, N., and Tenenblat, K., Laplace transformation in higher dimensions, Duke Mathematical Journal 84 (1996), 237–266 . [12] Moutard, Th. F., Sur la construction des équations de la forme z^ (−1) z_(xy) = λ(x, y), qui admettent une intégrale générale explicite, J. de L’Ecole Polytech. Cahier 45 (1878), 834. [13] Ushveridze, A., Quasi-exactly solvable models in quantum mechanics, IOP, Bristol, 1994. [14] Vassiliou, P. J., On some geometry associated with a generalised Toda lattice, Bull. Austral. Math. Soc. 49 (1994), 439–462. [15] Veselov, A. P., and and Novikov, S. P., Exactly solvable periodic two-dimensional Schrödinger operators, Uspekhi Mat. Nauk 50 (1995), 171–172. [16] Witten, E., Dynamical breaking of supersymmetry, Nucl. Phys. B188 (1981), 513–555. [17] Witten, E., Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982), 661–692. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc | |
| relation.isAuthorOfPublication.latestForDiscovery | 7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc |
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