Neumann-type expansion of Coulomb functions

Journal Article · Mon Feb 28 23:00:00 EST 1994 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1994.1042· OSTI ID:7156740

Marksteiner, P; Badralexe, E; Freeman, A J ^[1]

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1. Northwestern Univ., Evanston, IL (United States)

An expansion is derived for the regular (power series) part of the Coulomb function, G[sub o]([eta], [rho]), in terms of Whittaker functions, which are closely related to the regular Coulomb functions F[sub l]([eta], [rho]). The expansion coefficients are given as a sum of three terms; each of the terms obeys a simple three-term recurrence relation. In conjunction with the downward recurrence method for the regular functions (which is also discussed), this expansion is very useful for computing the irregular Coulomb functions G[sub l]([eta], [rho]), in particular for an attractive potential ([eta] < O) and for small or moderately large values of [rho]. 10 refs., 1 tab.

• OSTI ID: 7156740
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 111:1; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
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BESSEL FUNCTIONS
COMPUTERIZED SIMULATION
COULOMB FIELD
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
NEUMANN SERIES
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICS
SCHROEDINGER EQUATION
SERIES EXPANSION
SIMULATION
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