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Pseudospectral Methods For Differential Equations: Application To The Schrodingertype Eigenvalue ProblemsAlici, Haydar 01 December 2003 (has links) (PDF)
In this thesis, a survey on pseudospectral methods for differential equations is presented. Properties of the classical orthogonal polynomials required in this context are reviewed. Differentiation matrices corresponding to Jacobi, Laguerre,and Hermite cases are constructed. A fairly detailed investigation is made for the Hermite spectral methods, which is applied to the Schrö / dinger eigenvalue equation with several potentials. A discussion of the numerical results and comparison with other methods are then introduced to deduce the effciency of the method.
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Bose-einstein Condensation At Lower DimensionsOzdemir, Sevilay 01 January 2004 (has links) (PDF)
In this thesis, the properties of the Bose-Einstein condensation (BEC) in low dimensions are reviewed. Three dimensional weakly interacting Bose systems are examined by the variational method. The effects of both the attractive and the repulsive interatomic forces are studied. Thomas-Fermi approximation is applied to find the ground state energy and the chemical potential. The occurrence of the BEC in low dimensional systems, is studied for ideal gases confined by both harmonic and power-law potentials. The properties of BEC in highly anisotropic trap are investigated and the conditions for reduced dimensionality are derived.
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Structure of hypernuclei studied with the integrodifferential equations approachNkuna, John Solly 06 1900 (has links)
A two-dimensional integrodi erential equation resulting from the use of potential harmonics
expansion in the many-body Schr odinger equation is used to study ground-state
properties of selected few-body nuclear systems. The equation takes into account twobody
correlations in the system and is applicable to few- and many-body systems. The
formulation of the equation involves the use of the Jacobi coordinates to de ne relevant
global coordinates as well as the elimination of center-of-mass dependence. The form of
the equation does not depend on the size of the system. Therefore, only the interaction
potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon
potentials are employed to construct the Hamiltonian of the systems. The results obtained
are in good agreement with those obtained using other methods. / Physics / M.Sc. (Physics)
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Study Of One Dimensional Position Dependent Effective Mass Problem In Some Quantum Mechanical SystemsBucurgat, Mahmut 01 February 2008 (has links) (PDF)
The one dimensional position dependent effective mass problem is studied by solving the Schrö / dinger equation for some well known potentials, such as the deformed Hulthen, the Mie, the Kratzer, the pseudoharmonic, and the Morse potentials. Nikiforov-Uvarov method is used in the calculations
to get energy eigenvalues and the corresponding wave functions exactly. By introducing a free parameter in the transformation of the wave function, the position dependent effective mass problem is reduced to the solution
of the Schrö / dinger equation for the constant mass case. At the same time, the deformed Hulthen potential is solved for the position dependent effective mass case by applying the method directly. The Morse potential is also solved for a mass distribution function, such that the solution can be reduced to the constant mass case.
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Sobre uma classe de equações elípticas envolvendo crescimento exponencial em ℝ2Guimarães, Wanderson Rodrigo 16 May 2013 (has links)
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Previous issue date: 2013-05-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, we will study the existence and multiplicity of weak solutions for a
class of nonhomogeneous elliptic problems involving exponential growth Trudinger-Moser
type in R2. For this, we will use the Ekeland s Variational Principle and the Mountain
Pass Theorem without the Palais-Smale condition in combination with a version of the
Trudinger-Moser inequality. / Teorema do Passo da Montanha, Principio variacional de Ekeland,
equação de Schrodinger, Desigualdade de Trudinger-Moser, Crescimento Exponencial.
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