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Quadratic Algebras in Quantum Mechanics

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Dynamical symmetries prove extremely useful and have applications in many physical situationsl1. Customarily, these symmetries are described mathematically in terms of Lie groups and algebras. It has been appreciated howewer that more general structures can sometimes be required. A celebrated example is that of Lie superalgebras; these arise when supersymmetries are encountered. Another type of algebras, that of quantum groups, is also being recognized as potentially relevant to describe dynamical symmetries, especially in the context of integrable models. These quantum groups belong to the class of quadratic algebras which are defined by subjecting the generators to quadratic relations. The purpose of this paper is to provide a simple example where the symmetries are most naturally discussed using such a quadratic algebra.


  • Quantum Group
  • Frequency Ratio
  • Symmetry Algebra
  • Schrodinger Equation
  • Dynamical Symmetry

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© 1994 Springer Science+Business Media New York

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Létourneau, P., Vinet, L. (1994). Quadratic Algebras in Quantum Mechanics. In: Gruber, B., Otsuka, T. (eds) Symmetries in Science VII. Springer, Boston, MA.

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