dorsal/arxiv
View SchemaGeneralized Pseudopotentials for Higher Partial Wave Scattering
| Authors | Rene Stock, Andrew Silberfarb, Eric L. Bolda, Ivan H. Deutsch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405153 |
| URL | https://arxiv.org/abs/quant-ph/0405153 |
| DOI | 10.1103/PhysRevLett.94.023202 |
| Journal | Phys. Rev. Lett. 94, 023202 (2005) |
Abstract
We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher order multipole moments not accounted for with a monopolar delta function at the origin, as used in the familiar Fermi pseudopotential for s-wave scattering. By making the strength of the potential energy dependent, we derive self-consistent solutions for the entire energy spectrum of the realistic potential. We apply this to study two particles in an isotropic harmonic trap, interacting through a central potential, and derive analytic expressions for the energy eigenstates and eigenvalues.
{
"annotation_id": "30d4a054-4364-49f5-8560-41b708c116d6",
"date_created": "2026-03-02T18:02:06.877000Z",
"date_modified": "2026-03-02T18:02:06.877000Z",
"file_hash": "3abf52e1068d1e855df2f8dbe43611e5182666a7c0ace289d9ac0c4b504611d1",
"private": false,
"record": {
"abstract": "We derive a generalized zero-range pseudopotential applicable to all partial\nwave solutions to the Schroedinger equation based on a delta-shell potential in\nthe limit that the shell radius approaches zero. This properly models all\nhigher order multipole moments not accounted for with a monopolar delta\nfunction at the origin, as used in the familiar Fermi pseudopotential for\ns-wave scattering. By making the strength of the potential energy dependent, we\nderive self-consistent solutions for the entire energy spectrum of the\nrealistic potential. We apply this to study two particles in an isotropic\nharmonic trap, interacting through a central potential, and derive analytic\nexpressions for the energy eigenstates and eigenvalues.",
"arxiv_id": "quant-ph/0405153",
"authors": [
"Rene Stock",
"Andrew Silberfarb",
"Eric L. Bolda",
"Ivan H. Deutsch"
],
"categories": [
"quant-ph",
"cond-mat.soft",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevLett.94.023202",
"journal_ref": "Phys. Rev. Lett. 94, 023202 (2005)",
"title": "Generalized Pseudopotentials for Higher Partial Wave Scattering",
"url": "https://arxiv.org/abs/quant-ph/0405153"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5662b21e-d017-4513-b0e8-98bc9d36c9b6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}