dorsal/arxiv
View SchemaIs the CPT-norm always positive?
| Authors | Boris F Samsonov, Pinaki Roy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503040 |
| URL | https://arxiv.org/abs/quant-ph/0503040 |
| DOI | 10.1088/0305-4470/38/15/L02 |
| Journal | J. Phys. A: Math. Gen. 38 (2005) L249--L255 |
Abstract
We give an explicit example of an exactly solvable PT-symmetric Hamiltonian with the unbroken PT symmetry which has one eigenfunction with the zero PT-norm. The set of its eigenfunctions is not complete in corresponding Hilbert space and it is non-diagonalizable. In the case of a regular Sturm-Liouville problem any diagonalizable PT-symmetric Hamiltonian with the unbroken PT symmetry has a complete set of positive CPT-normalazable eigenfunctions. For non-diagonalizable Hamiltonians a complete set of CPT-normalazable functions is possible but the functions belonging to the root subspace corresponding to multiple zeros of the characteristic determinant are not eigenfunctions of the Hamiltonian anymore.
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"abstract": "We give an explicit example of an exactly solvable PT-symmetric Hamiltonian\nwith the unbroken PT symmetry which has one eigenfunction with the zero\nPT-norm. The set of its eigenfunctions is not complete in corresponding Hilbert\nspace and it is non-diagonalizable. In the case of a regular Sturm-Liouville\nproblem any diagonalizable PT-symmetric Hamiltonian with the unbroken PT\nsymmetry has a complete set of positive CPT-normalazable eigenfunctions. For\nnon-diagonalizable\n Hamiltonians a complete set of CPT-normalazable functions is possible but the\nfunctions belonging to the root subspace corresponding to multiple zeros of the\ncharacteristic determinant are not eigenfunctions of the Hamiltonian anymore.",
"arxiv_id": "quant-ph/0503040",
"authors": [
"Boris F Samsonov",
"Pinaki Roy"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/15/L02",
"journal_ref": "J. Phys. A: Math. Gen. 38 (2005) L249--L255",
"title": "Is the CPT-norm always positive?",
"url": "https://arxiv.org/abs/quant-ph/0503040"
},
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