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Boundary Conditions on Internal Three-Body Wave Functions

Kevin A. Mitchell·Robert G. Littlejohn
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Abstract

For a three-body system, a quantum wave function $Ψ^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $χ^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $χ^\ell_k$ to ensure that the external wave function $Ψ^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $χ^\ell_k$ 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 $r^{|m|}$ 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.

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Kevin A. Mitchell, Robert G. Littlejohn. 1999-08-18. Boundary Conditions on Internal Three-Body Wave Functions. https://doi.org/10.1103/physreva.61.042502

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