Estimates for eigenvalues of Sturm-Liouville operators with some PT-symmetric potentials

Year 2025, Volume: 54 Issue: 5, 1737 - 1757, 29.10.2025

Cemile Nur

https://doi.org/10.15672/hujms.1542854

Abstract

We provide some useful equations for calculating the periodic and antiperiodic eigenvalues of the one-dimensional Schrödinger operator $S(q)$ with a special potential that is a PT-symmetric trigonometric polynomial. We even give estimates to approximate complex eigenvalues by the roots of some polynomials derived from some iteration formulas. Moreover, we give a numerical example with error estimation using Rouche's theorem.

Keywords

eigenvalue estimations , periodic and antiperiodic boundary conditions , PT-symmetric potential

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