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Iterative method of solving schrodinger equation for non-Hermitian, pt-symmetric Hamiltonians

PT-symmetric Hamiltonians proposed by Bender and Boettcher can have real energy spectra. As an extension of the Hermitian Hamiltonian, PT-symmetric systems have attracted a great interest in recent years. Understanding the underlying mathematical structure of these theories sheds insight on outstanding problems of physics. These problems include the nature of Higgs particles, the properties of dark matter, the matter-antimatter asymmetry in the universe, and neutrino oscillations. Furthermore, PT-phase transition has been observed in lasers, optical waveguides, microwave cavities, superconducting wires and circuits. The objective of this thesis is to extend the iterative method of solving Schrodinger equation used for an harmonic oscillator systems to Hamiltonians with PT-symmetric potentials. An important aspect of this approach is the high accuracy of eigenvalues and the fast convergence. Our method is a combination of Hill determinant method [8] and the power series expansion. eigenvalues and the fast convergence. One can transform the Schrodinger equation into a secular equation by using a trial wave function. A recursion structure can be obtained using the secular equation, which leads to accurate eigenvalues. Energy values approach to exact ones when the number of iterations is increased. We obtained eigenvalues for a set of PT-symmetric Hamiltonians.

Identiferoai:union.ndltd.org:auctr.edu/oai:digitalcommons.auctr.edu:dissertations-4724
Date01 July 2016
CreatorsWijewardena, Udagamge
PublisherDigitalCommons@Robert W. Woodruff Library, Atlanta University Center
Source SetsAtlanta University Center
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceETD Collection for AUC Robert W. Woodruff Library

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