Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Green’s Function Related Abstracts

3 Theoretical Analysis of the Optical and Solid State Properties of Thin Film

Authors: E. I. Ugwu

Abstract:

Theoretical analysis of the optical and Solid State properties of ZnS thin film using beam propagation technique in which a scalar wave is propagated through the material thin film deposited on a substrate with the assumption that the dielectric medium is section into a homogenous reference dielectric constant term, and a perturbed dielectric term, representing the deposited thin film medium is presented in this work. These two terms, constitute arbitrary complex dielectric function that describes dielectric perturbation imposed by the medium of for the system. This is substituted into a defined scalar wave equation in which the appropriate Green’s Function was defined on it and solved using series technique. The green’s value obtained from Green’s Function was used in Dyson’s and Lippmann Schwinger equations in conjunction with Born approximation method in computing the propagated field for different input regions of field wavelength during which the influence of the dielectric constants and mesh size of the thin film on the propagating field were depicted. The results obtained from the computed field were used in turn to generate the data that were used to compute the band gaps, solid state and optical properties of the thin film such as reflectance, Transmittance and reflectance with which the band gap obtained was found to be in close approximate to that of experimental value.

Keywords: propagation, scalar wave, optical and solid state properties, thin film, dielectric medium, perturbation, Lippmann Schwinger equations, Green’s Function

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2 Solution of the Nonrelativistic Radial Wave Equation of Hydrogen Atom Using the Green's Function Approach

Authors: F. U. Rahman, R. Q. Zhang

Abstract:

This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s Function, hydrogen atom, Lippmann Schwinger equation, radial wave

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1 Green Function and Eshelby Tensor Based on Mindlin’s 2nd Gradient Model: An Explicit Study of Spherical Inclusion Case

Authors: A. Selmi, A. Bisharat

Abstract:

Using Fourier transform and based on the Mindlin's 2nd gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

Keywords: Green’s Function, Eshelby tensor, Eshelby-like tensor, Mindlin’s 2nd gradient model, spherical inclusion

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