×

zbMATH — the first resource for mathematics

Exactly solvable models in supersymmetric quantum mechanics and connection with spectrum-generating algebras. (English. Russian original) Zbl 0991.81033
Theor. Math. Phys. 118, No. 3, 285-294 (1999); translation from Teor. Mat. Fiz. 118, No. 3, 362-374 (1999).
Summary: Analytic expressions for the eigenvalues and eigenfunctions of nonrelativistic shape-invariant Hamiltonians can be derived using the well-known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess spectrum-generating algebras and are hence solvable by an independent group theory method. We demonstrate the equivalence of the two solution methods by developing an algebraic framework for shape-invariant Hamiltonians with a general parameter change involving nonlinear extensions of Lie algebras.

MSC:
81Q60 Supersymmetry and quantum mechanics
81U15 Exactly and quasi-solvable systems arising in quantum theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] F. Cooper, A. Khare, and U. Sukhatme,Phys. Rep.,251, 268 (1995). · doi:10.1016/0370-1573(94)00080-M
[2] L. Infeld and T. E. Hull,Rev. Mod. Phys.,23, 21 (1951); L. E. Gendenshtein,JETP Lett.,38, 356 (1983). · Zbl 0043.38602 · doi:10.1103/RevModPhys.23.21
[3] Y. Alhassid, F. Gürsey, and F. Iachello,Ann. Phys.,148, 346 (1983); J. Wu and Y. Alhassid,Phys. Rev. A,31, 557 (1990). · Zbl 0526.22018 · doi:10.1016/0003-4916(83)90244-0
[4] A. O. Barut, A. Inomata, and R. Wilson,J. Phys. A,20, 4075 (1987);20, 4083 (1987); M. J. Englefield,J. Math. Phys.,28, 827 (1987); M. J. Englefield and C. Quesne,J. Phys. A,24, 3557 (1987); R. D. Tangerman and J. A. Tjon,Phys. Rev. A,48, 1089 (1993). · doi:10.1088/0305-4470/20/13/016
[5] A. Gangopadhyaya and U. P. Sukhatme,Phys. Lett. A,224, 5 (1996); U. P. Sukhatme, C. Rasinariu, and A. Khare,Phys. Lett. A,234, 401 (1997); ”Cyclic shape-invariant potentials”, Preprint hep-ph/9706282 (1997). · Zbl 1037.81537 · doi:10.1016/S0375-9601(96)00807-9
[6] G. A. Natanzon,Theor. Math. Phys.,38, 146 (1979). · Zbl 0423.34033 · doi:10.1007/BF01016836
[7] A. Gangopadhyaya, J. V. Mallow, and U. P. Sukhatme, ”Shape invariance and its connection to potential algebra,” in:Supersymmetry and Integrable Models (Lect. Notes Phys., Vol. 502) (H. Aratyn et al., eds.), Springer, Berlin (1998), p. 341. · Zbl 0901.35081
[8] A. B. Balantekin,Phys. Rev. A,57, 4188 (1998); ”Algebraic approach to shape invariance,” Preprint quantph/9712018 (1997). · doi:10.1103/PhysRevA.57.4188
[9] M. Rocek,Phys. Lett. B,255, 554 (1991); T. Curtright and C. Zachos,Phys. Lett. B,243, 237 (1990); T. Curtright, G. Ghandour, and C. Zachos,J. Math. Phys.,32, 676 (1991). · doi:10.1016/0370-2693(91)90265-R
[10] A. Shabat,Inverse Prob.,8, 303 (1992); V. P. Spiridonov,Phys. Rev. Lett.,69, 398 (1992). · Zbl 0762.35098 · doi:10.1088/0266-5611/8/2/009
[11] D. Barclay, R. Dutt, A. Gangopadhyaya, A. Khare, A. Pagnamenta, and U. Sukhatme,Phys. Rev. A,48, 2786 (1993). · doi:10.1103/PhysRevA.48.2786
[12] S. Chaturvedi, R. Dutt, A. Gangopadhyaya, P. Panigrahi, C. Rasinariu, and U. Sukhatme,Phys. Lett. A,248, 109 (1998). · doi:10.1016/S0375-9601(98)00636-7
[13] A. Gangopadhyaya, J. V. Mallow, and U. P. Sukhatme, ”Shape invariance and inherent potential algebra”, to appear inPhys. Rev. A. · Zbl 0901.35081
[14] A. Gangopadhyaya, P. Panigrahi, and U. Sukhatme,Helv. Phys. Acta,67, 363 (1994).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.