Boundary conditions on internal three-body wave functions

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For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} 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 ... continued below

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42 pages

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Mitchell, Kevin A. & Littlejohn, Robert G. October 1, 1999.

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Description

For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} 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.

Physical Description

42 pages

Notes

OSTI as DE00841543

Source

  • Journal Name: Physical Review A; Journal Volume: 61; Journal Issue: 4; Other Information: Submitted to Physical Review A: Volume 61, No.4; Journal Publication Date: 04/2000

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  • Report No.: LBNL--44436
  • Report No.: HIFAN 1008
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 841543
  • Archival Resource Key: ark:/67531/metadc778756

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  • October 1, 1999

Added to The UNT Digital Library

  • Dec. 3, 2015, 9:30 a.m.

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  • April 4, 2016, 12:22 p.m.

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Mitchell, Kevin A. & Littlejohn, Robert G. Boundary conditions on internal three-body wave functions, article, October 1, 1999; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc778756/: accessed August 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.