Evaluation of the spherical Bessel transform of a Whittaker function: An application of a difference equation method

Journal Article · Mon Jun 01 04:00:00 EDT 1992 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529623· OSTI ID:7107074

Maximon, L C ^[1]

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1. Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, DC 20052 (United States)

A simple analytic expression for the spherical Bessel transform of the zero-range bound state wave function with the Coulomb interaction present, for the {ital l}th partial wave, expressed as a Whittaker function, is obtained. The result is given in terms of polynomials of degree {ital l}, the exponential function, and a simple hypergeometric function which is independent of {ital l}. Transformations of this latter function are derived in terms of more rapidly convergent series. The method presented has much wider application, since it relies essentially only on the existence of differential-difference equations for the functions involved, and the solution of the inhomogeneous difference and differential equations satisfied by the transform.

• DOE Contract Number: FG05-86ER40270
• OSTI ID: 7107074
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 33:6; ISSN 0022-2488; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BESSEL FUNCTIONS
BOUND STATE
COULOMB FIELD
ELECTRIC FIELDS
FUNCTIONS
HYPERGEOMETRIC FUNCTIONS
INTEGRAL TRANSFORMATIONS
PARTIAL WAVES
POLYNOMIALS
SERIES EXPANSION
TRANSFORMATIONS
WAVE FUNCTIONS