Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 060, 15 pages      arXiv:1209.2497      https://doi.org/10.3842/SIGMA.2012.060
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

Ladder Operators for Quantum Systems Confined by Dihedral Angles

Eugenio Ley-Koo a and Guo-Hua Sun b
a) Instituto de Física, Universidad Nacional Autónoma de México, México
b) Centro Universitario Valle de Chalco, Universidad Autónoma del Estado de México, México

Received June 29, 2012, in final form September 07, 2012; Published online September 12, 2012

Abstract
We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for the hydrogen atom in the same situation of confinement, in spherical, parabolic and prolate spheroidal coordinates. The actions of such operators on any eigenfunction are examined in the respective coordinates, illustrating the possibility of generating the complete bases of eigenfunctions in the respective coordinates for both physical systems. The relationships between the eigenfunctions in each pair of coordinates, and with the same eigenenergies are also illustrated.

Key words: Ladder operators; harmonic oscillator; hydrogen atom; confinement in dihedral angles.

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