dorsal/arxiv
View SchemaBoundary Conditions on Internal Three-Body Wave Functions
| Authors | Kevin A. Mitchell, Robert G. Littlejohn |
|---|---|
| Categories | |
| ArXiv ID | physics/9908037 |
| URL | https://arxiv.org/abs/physics/9908037 |
| DOI | 10.1103/PhysRevA.61.042502 |
Abstract
For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ 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.
{
"annotation_id": "ad0c8803-c81c-4510-af63-4701eb5cc6f4",
"date_created": "2026-03-02T18:01:25.182000Z",
"date_modified": "2026-03-02T18:01:25.182000Z",
"file_hash": "ba2434818a2305d9cb32576679806bb14843b774d58fd6bf5e781806b3ba7ab8",
"private": false,
"record": {
"abstract": "For a three-body system, a quantum wave function $\\Psi^\\ell_m$ with definite\n$\\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave\nfunction $\\chi^\\ell_k$ which is a function of three internal coordinates. This\narticle provides necessary and sufficient constraints on $\\chi^\\ell_k$ to\nensure that the external wave function $\\Psi^\\ell_m$ is analytic. These\nconstraints effectively amount to boundary conditions on $\\chi^\\ell_k$ and its\nderivatives at the boundary of the internal space. Such conditions find\nsimilarities in the (planar) two-body problem where the wave function (to\nlowest order) has the form $r^{|m|}$ at the origin. We expect the boundary\nconditions to prove useful for constructing singularity free three-body basis\nsets for the case of nonvanishing angular momentum.",
"arxiv_id": "physics/9908037",
"authors": [
"Kevin A. Mitchell",
"Robert G. Littlejohn"
],
"categories": [
"physics.chem-ph",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.61.042502",
"title": "Boundary Conditions on Internal Three-Body Wave Functions",
"url": "https://arxiv.org/abs/physics/9908037"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "60072664-ff69-4af2-92cb-87ee76e95788",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}