Algebraic methods, Bender-Wu formulas, and continued fractions at large order for charmonium

Journal Article · Mon Apr 01 04:00:00 EST 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.31.2054· OSTI ID:6025134

Vrscay, E R

A special coordinate realization of the Lie algebra so(4,2) is used to reformulate the perturbation problem of a hydrogen atom in a linear radial potential over a complete and discrete Sturmian basis. In this way, the Rayleigh-Schroedinger coefficients E/sub N/LM/sup( n/) may be calculated to arbitrarily high order for any state. The large-order behavior of these coefficients is determined by Bender-Wu WKB theory. A general formula for the large-order behavior of the coefficients c/sub n//sup N/LM of the Stieltjes continued-fraction representations of these perturbation expansions is given and related to that of the E/sub N/LM/sup( n/).

• Research Organization: Quantum Theory Group, Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L3G1
• OSTI ID: 6025134
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 31:4; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
CHARMONIUM
ELEMENTS
HYDROGEN
ISOELECTRONIC ATOMS
LIE GROUPS
NONMETALS
PERTURBATION THEORY
POTENTIALS
QUARKONIUM
RAYLEIGH-SCHROEDINGER FORMULA
SYMMETRY GROUPS
WKB APPROXIMATION