dorsal/arxiv
View SchemaDifferential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603023 |
| URL | https://arxiv.org/abs/quant-ph/0603023 |
| DOI | 10.1063/1.2212668 |
| Journal | J. Math. Phys. 47, 072103 (2006) |
Abstract
For a given pseudo-Hermitian Hamiltonian of the standard form: H=p^2/2m+v(x), we reduce the problem of finding the most general (pseudo-)metric operator \eta satisfying H^\dagger=\eta H \eta^{-1} to the solution of a differential equation. If the configuration space is the real line, this is a Klein-Gordon equation with a nonconstant mass term. We obtain a general series solution of this equation that involves a pair of arbitrary functions. These characterize the arbitrariness in the choice of \eta. We apply our general results to calculate \eta for the PT-symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials. For the first two systems, our method reproduces the known results in a straightforward and extremely efficient manner. For all these systems we obtain the most general \eta up to second order terms in the coupling constants.
{
"annotation_id": "946c01f9-043d-458d-9b14-6d3f4bcce393",
"date_created": "2026-03-02T18:02:23.674000Z",
"date_modified": "2026-03-02T18:02:23.674000Z",
"file_hash": "a5def16d4c8b14efa42048d6cda296cfd346e66cc5cde36d22b2f7cfba9cfa58",
"private": false,
"record": {
"abstract": "For a given pseudo-Hermitian Hamiltonian of the standard form: H=p^2/2m+v(x),\nwe reduce the problem of finding the most general (pseudo-)metric operator \\eta\nsatisfying H^\\dagger=\\eta H \\eta^{-1} to the solution of a differential\nequation. If the configuration space is the real line, this is a Klein-Gordon\nequation with a nonconstant mass term. We obtain a general series solution of\nthis equation that involves a pair of arbitrary functions. These characterize\nthe arbitrariness in the choice of \\eta. We apply our general results to\ncalculate \\eta for the PT-symmetric square well, an imaginary scattering\npotential, and a class of imaginary delta-function potentials. For the first\ntwo systems, our method reproduces the known results in a straightforward and\nextremely efficient manner. For all these systems we obtain the most general\n\\eta up to second order terms in the coupling constants.",
"arxiv_id": "quant-ph/0603023",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2212668",
"journal_ref": "J. Math. Phys. 47, 072103 (2006)",
"title": "Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein\u0027s field equation",
"url": "https://arxiv.org/abs/quant-ph/0603023"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b1047c5d-5ecd-4e22-ad21-26fe1ce6b2af",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}