On a Generalized D-Dimensional Oscillator: Interbasis Expansions
Abstract
This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases (transition matrix), and vice-versa, are found in terms of the SU(2) Clebsch--Gordan coefficients analytically continued to real values of their arguments. The diagram method, which allow one to construct a transition matrix for arbitrary dimension, is developed.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.