Finite two-dimensional oscillator: II. The radial model
Por:
Atakishiyev N.M., Pogosyan G.S., Vicent L.E., Wolf K.B.
Publicada:
1 ene 2001
Resumen:
A finite two-dimensional radial oscillator of (N + 1)2 points is proposed, with the dynamical Lie algebra s o (4) = s u (2)x ? s u (2)y examined in part I of this work, but reduced by a subalgebra chain s o (4) ? s o (3) ? s o (2). As before, there are a finite number of energies and angular momenta; the Casimir spectrum of the new chain provides the integer radii 0 ? ? ? N, and the 2? + 1 discrete angles on each circle ? are obtained from the finite Fourier transform of angular momenta. The wavefunctions of the finite radial oscillator are s o (3) Clebsch-Gordan coefficients. We define here the Hankel-Hahn transforms (with dual Hahn polynomials) as finite-N unitary approximations to Hankel integral transforms (with Bessel functions), obtained in the contraction limit N ? ?.
Filiaciones:
Atakishiyev N.M.:
Instituto de Matemáticas, UNAM, Apartado Postal 273-3, 62210 Cuernavaca, Morelos, Mexico
Pogosyan G.S.:
Centro de Ciencias Físicas, Univ. Nac. Auton. de Mexico, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico
Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russian Federation
Vicent L.E.:
Instituto de Matemáticas, UNAM, Apartado Postal 273-3, 62210 Cuernavaca, Morelos, Mexico
Centro de Ciencias Físicas, Univ. Nac. Auton. de Mexico, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico
Wolf K.B.:
Centro de Ciencias Físicas, Univ. Nac. Auton. de Mexico, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico
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