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

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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.
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  • [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.
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