An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation

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2019

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Kaya, Ruşen

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In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those resulting from the methods applied to the original formulation of the problem. Consecutive symmetries are observed throughout the symmetric structure of the problem, the symmetric Green’s function, the symmetric potentials used in the method and the symmetric matrices obtained eventually.

Subject Keywords

Integral equations., Integral Equations, Green’s Function, Schrödinger equation, Rayleigh- Ritz Method.

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http://etd.lib.metu.edu.tr/upload/12623440/index.pdf
https://hdl.handle.net/11511/43550

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

R. Kaya, “An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation,” Thesis (M.S.) -- Graduate School of Applied Mathematics. Mathematics., Middle East Technical University, 2019.