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ЖУРНАЛЫ // Математические заметки // Архив

Матем. заметки, 2023, том 114, выпуск 6, страницы 1401–1417 (Mi mzm14285)

Computing Periodic and Antiperiodic Eigenvalues with a PT-Symmetric Optical Potential

C. Nur

Department of Computer Engineering, Yalova University, Yalova, 77200 Türkiye

Аннотация: We give estimates for the eigenvalues of nonself-adjoint Sturm–Liouville operators with periodic and antiperiodic boundary conditions for the special potential $4\cos^{2}x+4iV\sin2x$ that is a PT-symmetric optical potential, especially when $|\sqrt{1-4V^{2}}|<3$ or equally $0\leq V<\sqrt{10}/2$. We provide some useful equations for calculating the periodic and antiperiodic eigenvalues. We even approximate complex eigenvalues by the roots of some polynomials derived from some iteration formulas. Moreover, we give a numerical example with error analysis.

Ключевые слова: eigenvalue estimate, periodic boundary conditions, antiperiodic boundary conditions, PT-symmetric optical potential.

Поступило: 26.11.2022
Исправленный вариант: 29.03.2023

Язык публикации: английский


 Англоязычная версия: Mathematical Notes, 2023, 114:6, 1401–1417

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