Hyperspherical elliptic harmonics and their relation to the Heun equation - art. no. 032510

Citation
Oi. Tolstikhin et M. Matsuzawa, Hyperspherical elliptic harmonics and their relation to the Heun equation - art. no. 032510, PHYS REV A, 6303(3), 2001, pp. 2510
Citations number
39
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW A
ISSN journal
10502947 → ACNP
Volume
6303
Issue
3
Year of publication
2001
Database
ISI
SICI code
1050-2947(200103)6303:3<2510:HEHATR>2.0.ZU;2-E
Abstract
Hyperspherical elliptic (HSE) harmonics are the eigenfunctions of the gener alized angular momentum operator obtained by separating variables in HSE co ordinates. These functions depend on accessory parameters characterizing th e HSE coordinate system and present a more flexible basis on a hypersphere as compared with more familiar hyperspherical polar harmonics. We discuss a special set of HSE harmonics arising in hyperspherical treatments of the t hree-body problem in the HSE coordinate system introduced in an earlier pap er [Tolstikhin et al., Phys. Rev. Lett. 74, 3573 (1995)]. The separation of variables in these coordinates leads to the Heun equation, which is a gene ralization of the Gauss hypergeometric equation. We develop an efficient me thod to solve the corresponding one-dimensional eigenvalue problem and thus construct the HSE harmonics, which opens a way for their application in th e studies of various atomic, molecular, and nuclear three-body systems.