dorsal/arxiv
View SchemaReflectionless Potentials and PT Symmetry
| Authors | Zafar Ahmed, Carl M. Bender, M. V. Berry |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508117 |
| URL | https://arxiv.org/abs/quant-ph/0508117 |
| DOI | 10.1088/0305-4470/38/39/L01 |
| Journal | J.Phys.A38:L627-L630,2005 |
Abstract
Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar product. The eigenvalues are determined by differential equations with boundary conditions imposed in wedges in the complex plane. For a special class of such systems, it is possible to impose the PT-symmetric boundary conditions on the real axis, which lies on the edges of the wedges. The PT-symmetric spectrum can then be obtained by imposing the more transparent requirement that the potential be reflectionless.
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"abstract": "Large families of Hamiltonians that are non-Hermitian in the conventional\nsense have been found to have all eigenvalues real, a fact attributed to an\nunbroken PT symmetry. The corresponding quantum theories possess an\nunconventional scalar product. The eigenvalues are determined by differential\nequations with boundary conditions imposed in wedges in the complex plane. For\na special class of such systems, it is possible to impose the PT-symmetric\nboundary conditions on the real axis, which lies on the edges of the wedges.\nThe PT-symmetric spectrum can then be obtained by imposing the more transparent\nrequirement that the potential be reflectionless.",
"arxiv_id": "quant-ph/0508117",
"authors": [
"Zafar Ahmed",
"Carl M. Bender",
"M. V. Berry"
],
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"quant-ph",
"hep-th"
],
"doi": "10.1088/0305-4470/38/39/L01",
"journal_ref": "J.Phys.A38:L627-L630,2005",
"title": "Reflectionless Potentials and PT Symmetry",
"url": "https://arxiv.org/abs/quant-ph/0508117"
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