Abstract:
We obtain an explicit expression for the ring-shaped matrix relating the ring-shaped functions corresponding to different values of an axiality parameter and find the relation between this matrix and the Wigner 6j-symbols. We investigate the motion of a quantum particle in a ring-shaped model with a zero “bare” potential and find bases factored in spherical and cylindrical coordinates for this model. We derive a formula generalizing the Rayleigh expansion for a plane wave in terms of spherical waves in a ring-shaped model.
This publication is cited in the following 3 articles:
L. G. Mardoyan, “Bases and interbasis expansions in the generalized MIC–Kepler problem in the continuous spectrum and the scattering problem”, Theoret. and Math. Phys., 217:2 (2023), 1661–1672
Marvin A Maulion, M Victoria Carpio-Bernido, Christopher C Bernido, “Jacobi partial waves for a set of 3D noncentral rational scatterers”, Phys. Scr., 98:1 (2023), 015202
Rampho G.J., “Lagrange-Mesh Solution of the Schrodinger Equation in Generalized Spherical Coordinates”, J. Phys. Commun., 2:3 (2018), UNSP 035037