dorsal/arxiv
View SchemaKinetic energy operator approach to the quantum three-body problem with Coulomb interactions
| Authors | Xuguang Chi, Wuyi Hsiang, Ping Sheng |
|---|---|
| Categories | |
| ArXiv ID | physics/0602139 |
| URL | https://arxiv.org/abs/physics/0602139 |
| DOI | 10.1016/j.ssc.2006.10.031 |
Abstract
We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body Laplacian operator with the respective masses. Through a four-step reduction process, the nine dimensional problem is reduced to a one dimensional coupled system of ordinary differential equations, amenable to accurate numerical solution as an infinite-dimensional algebraic eigenvalue problem. A key observation in this reduction process is that in the functional subspace of the kinetic energy operator where all the rotational degrees of freedom have been projected out, there is an intrinsic symmetry which can be made explicit through the introduction of Jacobi-spherical coordinates. A numerical scheme is presented whereby the Coulomb matrix elements are calculated to a high degree of accuracy with minimal effort, and the truncation of the linear equations is carried out through a systematic procedure
{
"annotation_id": "1afd16a6-4fd8-44c0-81ee-8fd283b231d3",
"date_created": "2026-03-02T18:01:07.843000Z",
"date_modified": "2026-03-02T18:01:07.843000Z",
"file_hash": "80f0a0c86d86c25f63d3c596456f0872dc19975b44ceaeadcba5e0db8d3ae4bc",
"private": false,
"record": {
"abstract": "We present a non-variational, kinetic energy operator approach to the\nsolution of quantum three-body problem with Coulomb interactions, based on the\nutilization of symmetries intrinsic to the kinetic energy operator, i.e., the\nthree-body Laplacian operator with the respective masses. Through a four-step\nreduction process, the nine dimensional problem is reduced to a one dimensional\ncoupled system of ordinary differential equations, amenable to accurate\nnumerical solution as an infinite-dimensional algebraic eigenvalue problem. A\nkey observation in this reduction process is that in the functional subspace of\nthe kinetic energy operator where all the rotational degrees of freedom have\nbeen projected out, there is an intrinsic symmetry which can be made explicit\nthrough the introduction of Jacobi-spherical coordinates. A numerical scheme is\npresented whereby the Coulomb matrix elements are calculated to a high degree\nof accuracy with minimal effort, and the truncation of the linear equations is\ncarried out through a systematic procedure",
"arxiv_id": "physics/0602139",
"authors": [
"Xuguang Chi",
"Wuyi Hsiang",
"Ping Sheng"
],
"categories": [
"physics.comp-ph",
"physics.atom-ph"
],
"doi": "10.1016/j.ssc.2006.10.031",
"title": "Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions",
"url": "https://arxiv.org/abs/physics/0602139"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "90bc39d9-157c-40ee-b7e1-8dfd95a8f80f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}