Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Download
index.pdf
Date
2019
Author
Kaya, Ruşen
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
114
views
67
downloads
Cite This
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.
URI
http://etd.lib.metu.edu.tr/upload/12623440/index.pdf
https://hdl.handle.net/11511/43550
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind
Kaya, Ruşen; Taşeli, Hasan (2022-01-01)
A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...
On the consistency of the solutions of the space fractional Schrodinger equation
Bayin, Selcuk S. (2012-04-01)
Recently, it was pointed out that the solutions found in the literature for the space fractional Schrodinger equation in a piecewise manner are wrong, except the case with the delta potential. We re-analyze this problem and show that an exact and a proper treatment of the relevant integral prove otherwise. We also discuss effective potential approach and present a free particle solution for the space and time fractional Schrodinger equation in general coordinates in terms of Fox's H-functions. (C) 2012 Amer...
On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems
Ergül, Özgür Salih (null; 2006-11-10)
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL funct...
An integral equation approach to the computation of nonlinear fields in electrical machines
Kükrer, Osman; Ertan, H. Bülnet (Institute of Electrical and Electronics Engineers (IEEE), 1988-7)
A numerical method based on an integral equation formulation, for the computation of nonlinear magnetostatic field, in two dimensions in cylindrical polar coordinates is given. The correctness of the method is illustrated by solving two linear two-dimensional magnetic field problems which have readily available analytical solutions. The dependence of the accuracy of the solution on the number and distribution of the meshes is studied on these examples. The method is then applied to the computation of the no...
Novel strategies for second-kind integral equations to analyze perfect electric conductors
Güler, Sadri; Ergül, Özgür Salih; Department of Electrical and Electronics Engineering (2019)
In this thesis, the magnetic-field integral equation (MFIE) for three-dimensional perfectly conducting objects is studied with a particular focus on the solutions of the formulation with the method of moments employing low-order discretization elements. Possible discretization functions and their applications in the testing of MFIE while considering different numbers of testing points are analyzed for accurate and efficient solutions. Successful results are obtained by using rotational Buffa-Christiansen te...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.