Quasi-exactly solvable spin 1/2 Schrödinger operators
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.contributor.author | Rodríguez González, Miguel Ángel | |
| dc.date.accessioned | 2023-06-20T20:08:45Z | |
| dc.date.available | 2023-06-20T20:08:45Z | |
| dc.date.issued | 1997-06 | |
| dc.description | ©1997 American Institute of Physics. The authors would like to acknowledge the partial financial support of the DGICYT under grant no. PB95-0401. | |
| dc.description.abstract | The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave functions with polynomial components to be equivalent to a Schrodinger operator are found. Systematic simplifications of these conditions are analyzed, and are then applied to the construction of new examples of multi-parameter QES spin 1/2 Hamiltonians in one dimension. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/31409 | |
| dc.identifier.doi | 10.1063/1.532020 | |
| dc.identifier.issn | 0022-2488 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1063/1.532020 | |
| dc.identifier.relatedurl | http://scitation.aip.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59671 | |
| dc.issue.number | 6 | |
| dc.journal.title | Journal of mathematical physics | |
| dc.language.iso | eng | |
| dc.page.final | 2811 | |
| dc.page.initial | 2795 | |
| dc.publisher | American Institute of Physics | |
| dc.relation.projectID | PB95-0401 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Quasi-exactly solvable spin 1/2 Schrödinger operators | |
| dc.type | journal article | |
| dc.volume.number | 38 | |
| dcterms.references | [1] M.A. Olshanetskii and A.M. Perelomov, “Quantum integrable systems related to Lie algebras", Phys. Rep. 94, 313-404 (1983). [2] A.V. Turbiner, “Quasi-exactly solvable problems and sl(2) algebra", Commun. Math. Phys. 118, 467-74 (1988). [3] A.G. Ushveridze, “Quasi-exactly solvable models in quantum mechanics", Sov. J. Part. Nucl. 20, 504{28 (1989). [4] M.A. Shifman, “New findings in quantum mechanics (partial algebraization of the spectral problem)", Int. J. Mod. Phys. A4, 2897-952 (1989). [5] A. González-López, N. Kamran, and P.J. Olver, “Normalizability of one-dimensional quasi- exactly solvable Schrödinger operators", Commun. Math. Phys. 153, 117-46 (1993). [6] M.A. Shifman and A.V. Turbiner, “Quantal problems with partial algebraization of the spectrum", Commun. Math. Phys. 126, 347-65 (1989). [7] Y. Brihaye and P. Kosinski, “Quasi exactly solvable 2 x 2 matrix equations", J. Math. Phys. 35, 3089-98 (1994). [8] Y. Brihaye, S. Giller, C. Gonera, and P. Kosinski, “The algebraic structures of quasi exactly solvable systems" (preprint, 1994). [9] A. González-López, N. Kamran, and P.J. Olver, “Quasi-exact solvability", Contemp. Math. 160, 113-40 (1994). [10] W. Miller, Jr., Lie Theory and Special Functions (Academic Press, New York, 1968). [11] N. Kamran and P.J. Olver, “Lie algebras of differential operators and Lie-algebraic potentials", J. Math. Anal. Appl. 145, 342-56 (1990). [12] A. González-López, N. Kamran, and P.J. Olver, “Quasi-exactly solvable Lie algebras of first order differential operators in two complex variables", J. Phys. A24, 3995-4008 (1991). [13] A. González-López, N. Kamran, and P.J. Olver, “Lie algebras of differential operators in two complex variables", American J. Math. 114, 1163-85 (1992). [14] A. González-López, N. Kamran, and P.J. Olver, “Real Lie algebras of differential operators and quasi-exactly solvable potentials", Phil. Trans. R. Soc. Lond. A 354, 1165-93 (1996). [15] A.V. Turbiner, “Lie algebraic approach to the theory of polynomial solutions. I. Ordinary differential equations and finite-difference equations in one variable" (CPT-92/P.2679-REV preprint, 1992). [16] A.V. Turbiner, “Lie algebraic approach to the theory of polynomial solutions. II. Differential equations in one real and one Grassmann variables and 2 x 2 matrix di erential equations" (ETH-TH/92-21 preprint, 1992). [17] A.V. Turbiner, “Lie algebras, cohomologies, and new findings in Quantum Mechanics", Contemp. Math. 160, 263-310 (1994). [18] H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950). [19] C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw Hill, New York, 1980). [20] R.P. Feynman and M. Gell-Mann, “Theory of the Fermi interaction", Phys. Rev. 109, 193-8 (1958). [21] Y. Brihaye, N. Devaux and P. Kosinski, “Central potentials and examples of hidden algebra structure", Int. J. Mod. Phys. A10, 4633-9 (1995). [22] P.J. Olver, Equivalence, Invariants and Symmetry (Cambridge University Press, Cambridge U.K., 1995). [23] G.B. Gurevich, Foundations of the Theory of Algebraic Invariants (P. Noordho , Groningen, Holland, 1964). [24] A. Galindo and P. Pascual, Quantum Mechanics I (Springer-Verlag, Berlin, 1990). | |
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| relation.isAuthorOfPublication.latestForDiscovery | 207092a4-0443-4336-a037-15936f8acc25 |
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