Improved WKB radial wave functions in several bases

Journal Article · Thu May 01 04:00:00 EDT 1986 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.33.2887· OSTI ID:5878213

Durand, B; Durand, L

We develop approximate WKB-like solutions to the radial Schroedinger equation for problems with an angular momentum barrier using Riccati-Bessel, Coulomb, and harmonic-oscillator functions as basis functions. The solutions treat the angular momentum singularity near the origin more accurately in leading approximation than the standard WKB solutions based on sine waves. The solutions based on Riccati-Bessel and free Coulomb wave functions continue smoothly through the inner turning point and are appropriate for scattering problems. The solutions based on oscillator and bound Coulomb wave functions incorporate both turning points smoothly and are particularly appropriate for bound-state problems; no matching of piecewise solutions using Airy functions is necessary.

• Research Organization: Los Alamos National Laboratory, Los Alamos, New Mexico 87545; Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
• DOE Contract Number: AC02-76ER00881
• OSTI ID: 5878213
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 33:5; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INTERACTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
POTENTIALS
QUARK-ANTIQUARK INTERACTIONS
SCHROEDINGER EQUATION
SINGULARITY
WAVE EQUATIONS
WAVE FUNCTIONS
WKB APPROXIMATION