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On q-analogues of the quantum harmonic oscillator and the quantum group \(SU(2)_ q\). (English) Zbl 0722.17009
From the introduction: “Here we wish to generalize to \(SU(2)_ q\), the simplest quantum group, the q-deformation of the Lie algebra of SU(2), Schwinger’s approach [J. Schwinger, On angular momentum’, in ‘Quantum Theory of Angular Momentum (ed. by L. C. Biedenharn and H. van Dam), Academic Press, 1965, p. 229-279] to the quantum theory of angular momentum. To achieve this, a q-deformation of the quantum harmonic oscillator formalism has to be developed. Much of the present paper is devoted to this task. Then the algebra of \(SU(2)_ q\), and its representations can be realized in terms of the variables of two independent q-deformed harmonic oscillators. Our results involve explicit coordinate of wavefunctions representations as well as abstract Hilbert space versions.”

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
53D50 Geometric quantization
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