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The quantum deformation of SU(1, 1) as the dynamical symmetry of the anharmonic oscillator

par Narganes-Quijano, Francisco
Référence Journal of Physics A: Mathematical and General, 24, 8, page (1699-1707), 013
Publication Publié, 1991

Article révisé par les pairs

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Résumé :

As an application of q-deformed algebras to standard quantum mechanics, the author shows that the SU(1, 1) dynamical symmetry of the quantum harmonic oscillator is deformed, in the first order of approximation, to the dynamical symmetry defined by the quantized universal enveloping algebra of SU(1, 1) when the harmonic potential is perturbed with a potential in x4. The resolution of the anharmonic oscillator is carried out algebraically in terms of generalized lowering and rising operators.