On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics Full article
| Journal |
Annales Henri Poincare
ISSN: 1424-0661 |
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| Output data | Year: 2024, Volume: 25, Pages: 3899–3909 Pages count : 11 DOI: 10.1007/s00023-024-01414-5 | ||||
| Tags | 81q05, 81q12, 81u20, 81u40, theoretical, mathematical and computational physics, dynamical systems and ergodic theory, quantum physics, mathematical methods in physics, classical and quantum gravitation, relativity theory, elementary particles, quantum field theory | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
We consider the Schr¨odinger operator with regular short range complex-valued potential in dimension d ≥ 1. We show that, for d ≥ 2, the unitarity of scattering operator for this Hamiltonian at high energies implies the reality of the potential (that is Hermiticity of Hamiltonian). In contrast, for d = 1, we present complex-valued exponentially localized soliton potentials with unitary scattering operator for all positive energies and with unbroken PT symmetry. We also present examples of complexvalued regular short range potentials with real spectrum for d = 3. Some directions for further research are formulated.
Cite:
Novikov R.G.
, Taimanov I.A.
On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics
Annales Henri Poincare. 2024. V.25. P.3899–3909. DOI: 10.1007/s00023-024-01414-5 WOS Scopus РИНЦ OpenAlex
On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics
Annales Henri Poincare. 2024. V.25. P.3899–3909. DOI: 10.1007/s00023-024-01414-5 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Mar 2, 2023 |
| Accepted: | Jan 4, 2024 |
| Published online: | Feb 5, 2024 |
| Published print: | Feb 26, 2024 |
Identifiers:
| Web of science: | WOS:001158125300001 |
| Scopus: | 2-s2.0-85184155329 |
| Elibrary: | 65987569 |
| OpenAlex: | W4321994397 |