dorsal/arxiv
View SchemaEigenvalue problems for the complex PT-symmetric potential V(x)= igx
| Authors | Zafar Ahmed |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609219 |
| URL | https://arxiv.org/abs/quant-ph/0609219 |
| DOI | 10.1016/j.physleta.2006.11.057 |
Abstract
The spectrum of complex PT-symmetric potential, $V(x)=igx$, is known to be null. We enclose this potential in a hard-box: $V(|x| \ge 1) =\infty $ and in a soft-box: $V(|x|\ge 1)=0$. In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic eigenvalues behave as $E_n \sim n^2.$ The solvable purely imaginary PT-symmetric potentials vanishing asymptotically known so far do not have real discrete spectrum. Our solvable soft-box potential possesses two real negative discrete eigenvalues if $|g|<(1.22330447)$. The soft-box potential turns out to be a scattering potential not possessing reflectionless states.
{
"annotation_id": "0917e9c2-e8db-4a04-9cbc-d97ed7488def",
"date_created": "2026-03-02T18:02:31.140000Z",
"date_modified": "2026-03-02T18:02:31.140000Z",
"file_hash": "2c4782e0c6b5907fc138b3499277c992980604a5b27b63229198a690646ced93",
"private": false,
"record": {
"abstract": "The spectrum of complex PT-symmetric potential, $V(x)=igx$, is known to be\nnull. We enclose this potential in a hard-box: $V(|x| \\ge 1) =\\infty $ and in a\nsoft-box: $V(|x|\\ge 1)=0$. In the former case, we find real discrete spectrum\nand the exceptional points of the potential. The asymptotic eigenvalues behave\nas $E_n \\sim n^2.$ The solvable purely imaginary PT-symmetric potentials\nvanishing asymptotically known so far do not have real discrete spectrum. Our\nsolvable soft-box potential possesses two real negative discrete eigenvalues if\n$|g|\u003c(1.22330447)$. The soft-box potential turns out to be a scattering\npotential not possessing reflectionless states.",
"arxiv_id": "quant-ph/0609219",
"authors": [
"Zafar Ahmed"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physleta.2006.11.057",
"title": "Eigenvalue problems for the complex PT-symmetric potential V(x)= igx",
"url": "https://arxiv.org/abs/quant-ph/0609219"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "31d71722-d198-41b2-85fa-85c4e37d6a27",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}