dorsal/arxiv
View SchemaLevinson's Theorem for the Klein-Gordon Equation in Two Dimensions
| Authors | Shi-Hai Dong, Xi-Wen Hou, Zhong-Qi Ma |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9808038 |
| URL | https://arxiv.org/abs/quant-ph/9808038 |
| DOI | 10.1103/PhysRevA.59.995 |
Abstract
The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.
{
"annotation_id": "9564ac00-3d33-4c9a-9284-738f7bf4dd87",
"date_created": "2026-03-02T18:02:45.251000Z",
"date_modified": "2026-03-02T18:02:45.251000Z",
"file_hash": "37f499a85cbe5e89280ecae8b605a4973fe91b09ea7999c9b9d2f115d9fa0a1e",
"private": false,
"record": {
"abstract": "The two-dimensional Levinson theorem for the Klein-Gordon equation with a\ncylindrically symmetric potential $V(r)$ is established. It is shown that\n$N_{m}\\pi=\\pi (n_{m}^{+}-n_{m}^{-})=\n[\\delta_{m}(M)+\\beta_{1}]-[\\delta_{m}(-M)+\\beta_{2}]$, where $N_{m}$ denotes\nthe difference between the number of bound states of the particle $n_{m}^{+}$\nand the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and\nthe $\\delta_{m}$ is named phase shifts. The constants $\\beta_{1}$ and\n$\\beta_{2}$ are introduced to symbol the critical cases where the half bound\nstates occur at $E=\\pm M$.",
"arxiv_id": "quant-ph/9808038",
"authors": [
"Shi-Hai Dong",
"Xi-Wen Hou",
"Zhong-Qi Ma"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.59.995",
"title": "Levinson\u0027s Theorem for the Klein-Gordon Equation in Two Dimensions",
"url": "https://arxiv.org/abs/quant-ph/9808038"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d0cc656b-038f-4cd1-b496-b10c7084727b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}