4.3 Article

Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

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Article Mathematics, Applied

Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

Cemile Nur

Summary: This paper investigates the eigenvalues of non-self-adjoint Sturm-Liouville operators with Dirichlet boundary conditions for a PT-symmetric optical potential, particularly when |c|=| root 1-4V(2)<2 or correspondingly 0 <= V < root 5-/2. Estimates for the eigenvalues are provided, and the results are compared with the periodic and antiperiodic eigenvalues of the Schr & ouml;dinger operator. The complex eigenvalues are approximated using the roots of polynomials, and a numerical example with error analysis is presented.

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