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- Title
The spectrum of the Hamiltonian with a PT-symmetric periodic optical potential.
- Authors
Veliev, O. A.
- Abstract
We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with potential , where We prove that the second critical point , after which the real parts of the first and second bands disappear, is a number between and . Moreover, we prove that is the degeneration point for the first periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary precise value of the second critical point as well as the th critical points after which the real parts of the th and th bands disappear, where
- Subjects
HAMILTONIAN operator; NUCLEAR optical potentials; ELECTRONIC band structure; MATHEMATICAL proofs; CRITICAL point (Thermodynamics)
- Publication
International Journal of Geometric Methods in Modern Physics, 2018, Vol 15, Issue 1, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887818500081