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

• Autorzy: Constantin Rasinariu , Jeffry Mallow , Asim Gangopadhyaya
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Supersymmetric quantum mechanics; shape invariance; potential algebra; spectrum-generating algebra

• Czasopismo: Open Physics
• Rocznik: 2007
• Tom: 5
• Numer: 2
• Strony: 111-134

Daty

wydano

2007-06-01

online

2007-02-02

Twórcy

autor

Constantin Rasinariu

• Department of Science and Mathematics, Columbia College Chicago, Chicago, USA,

autor

Jeffry Mallow

• Department of Physics, Loyola University Chicago, Chicago, USA,

autor

Asim Gangopadhyaya

• Department of Physics, Loyola University Chicago, Chicago, USA,

Bibliografia

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• [16] S.-H. Dong and Z.-Q. Ma: “The hidden symmetry for a quantum system with an infinitely deep square-well potential”, Am. J. Phys., Vol. 70, (2002), pp. 520–521. http://dx.doi.org/10.1119/1.1456073[Crossref]
• [17] W. Pauli: “Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik”, Z. Physik, Vol. 36, (1926), pp. 336–363; V. Fock: “Zur Theorie des Wasserstoffatoms”, Z. Physik, Vol. 98, (1935), pp. 145–154 http://dx.doi.org/10.1007/BF01450175[Crossref]
• [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]
• [19] A.B. Balantekin: “Algebraic approach to shape invariance”, Phys. Rev. A, Vol. 57, (1998), pp. 4188–4191. http://dx.doi.org/10.1103/PhysRevA.57.4188[Crossref]
• [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.
• [24] R. Dutt, A. Gangopadhyaya, C. Rasinariu and U. Sukhatme: “Coordinate Realizations of Deformed Lie Algebras with Three Generators”, Phys. Rev., Vol. A60, (1999), pp. 3482–3486.
• [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.

Identyfikatory

DOI

10.2478/s11534-007-0001-1