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2007 | 5 | 2 | 111-134
Article title

Exactly solvable problems of quantum mechanics and their spectrum generating algebras: A review

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EN
Abstracts
EN
In this review, we summarize the progress that has been made in connecting supersymmetry and spectrum generating algebras through the property of shape invariance. This monograph is designed to be used by our fellow researchers, by other interested physicists, and by students at the graduate and even undergraduate levels who would like a brief introduction to the field.
Publisher
Journal
Year
Volume
5
Issue
2
Pages
111-134
Physical description
Dates
published
1 - 6 - 2007
online
2 - 2 - 2007
References
  • [1] For Dirac’s ladder method, see P.A.M. Dirac: The Principles of Quantum Mechanics, 4th ed., Clarendon Press, Oxford, 1958.
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  • [12] J. Wu, Y. Alhassid and F. Gürsey: “Group theory approach to scattering. IV. Solvable potentials associated with SO(2,2)”, Ann. Phys., Vol. 196, (1989), pp. 163–181. http://dx.doi.org/10.1016/0003-4916(89)90049-3[Crossref]
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  • [18] R. Dutt, A. Gangopadhyaya and U. Sukhatme: “Noncentral potentials and spherical harmonics using supersymmetry and shape invariance”, Am. J. Phys., Vol. 65, (1996), pp. 400–403. http://dx.doi.org/10.1119/1.18551[Crossref]
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  • [20] A. Gangopadhyaya, J.V. Mallow and U.P. Sukhatme: “Exact solutions of the Schroedinger equation: Connection between supersymmetric quantum mechanics and spectrum generating algebras”, Phys. Rev. A, Vol. 58, (1998), pp. 4287–4292. http://dx.doi.org/10.1103/PhysRevA.58.4287[Crossref]
  • [21] A. Gangopadhyaya, J.V. Mallow, C. Rasinariu and U.P. Sukhatme: “Exact solutions of the Schroedinger equation: Connection between supersymmetric quantum mechanics and spectrum generating algebras”, Chinese J. Phys., Vol. 39, (2001), pp. 101–121.
  • [22] S. Chaturvedi, R. Dutt, A. Gangopadhyaya, P. Panigrahi, C. Rasinariu and U. Sukhatme: “Algebraic Shape Invariant Models”, Phys. Lett., Vol. A248, (1998), pp. 109–113.
  • [23] A. Gangopadhyaya, J.V. Mallow and U.P. Sukhatme: “Shape invariance and its connection to potential algebra”, In: Henrik Aratyn et al. (Eds.): Proceedings of Workshop on Supersymmetric Quantum Mechanics and Integrable Models, Springer-Verlag, Berlin, 1997.
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  • [25] For a very readable introduction to so(2, 1)-algebra and its representation, see B.G. Adams, J. Cizeka and J. Paldus: “Lie Algebraic Methods And Their Applications to Simple Quantum Systems”, In: P-O. Löwdin (Ed.): Advances in Quantum Chemistry, Vol. 19, Academic Press, New York, 1987.
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  • [27] A. Gangopadhyaya, J.V. Mallow and U.P. Sukhatme: “Broken Supersymmetric Shape Invariant Systems and Their Potential Algebras”, Phys. Lett., Vol. A283, (2001), pp. 279–284.
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-007-0001-1
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