On a Quantization of the Classical θ-Functions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On a Quantization of the Classical θ-Functions
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| Creator |
Brezhnev, Y.V.
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| Description |
The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find corresponding Poisson brackets. Availability of these ingredients allows us to state the problem of a canonical quantization to these equations and disclose some important problems. In a particular case the problem is completely solvable in the sense that spectrum of the Hamiltonian can be found. The spectrum is continuous, has a band structure with infinite number of lacunae, and is determined by the Mathieu equation: the Schrödinger equation with a periodic cos-type potential.
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| Date |
2019-02-12T20:34:07Z
2019-02-12T20:34:07Z 2015 |
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| Type |
Article
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| Identifier |
On a Quantization of the Classical θ-Functions / Y.V. Brezhnev // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 19 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 14H70; 33E05; 33E10; 37N20; 37J35; 81S10 DOI:10.3842/SIGMA.2015.035 http://dspace.nbuv.gov.ua/handle/123456789/147012 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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