Boundary conditions on internal three-body wave functions

Journal Article · Sat Apr 01 04:00:00 EST 2000 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.61.042502· OSTI ID:20215822

Mitchell, Kevin A ^[1]; Littlejohn, Robert G ^[1]

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1. Department of Physics, University of California, Berkeley, California 94720 (United States)

For a three-body system, a quantum wave function {psi}{sub m}{sup l} with definite l and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup l}, which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup l} to ensure that the external wave function {psi}{sub m}{sup l} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup l} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum. (c) 2000 The American Physical Society.

• OSTI ID: 20215822
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 61; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR MOMENTUM
BOUNDARY CONDITIONS
ELECTRONIC STRUCTURE
QUANTUM MECHANICS
THEORETICAL DATA
THREE-BODY PROBLEM
WAVE FUNCTIONS