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Solution of integral equations for separable interactions
Hvizdoš, Dávid ; Horáček, Jiří (advisor) ; Kolorenč, Přemysl (referee)
Title: Solution of integral equations for separable interactions Author: Dávid Hvizdoš Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Jiří Horáček, DrSc., Institute of Theoretical Physics Abstract: This work deals with the most fundamental types of integral equations (Fredholm and Volterra). Their occurrence in quantum mechanics is illustrated and the process that leads to the so-called regular and Jost solution is presented. Further their solutions in the case of separable interactions are studied. Analytical solutions on model separable potentials are sought. Analytical extensions of these solutions to the complex energy plane are provided and the properties of these functions are examined. The method of analytical continuation in the coupling constant based on the extension of the coupling constant as a function of is introduced. For some examples of separable potentials the Taylor expansion of the function and from it the inverse series √ are calculated. These series are then used to determine the resonance parameters of the potential and the accuracy of these calculations is discussed. Key words: integral equations, scattering theory, resonances, separable potential
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Modeling the dissociative recombination of light ions
Hvizdoš, Dávid ; Čurík, Roman (advisor) ; Kaprálová-Žďánská, Petra R. (referee) ; Kokoouline, Viatcheslav (referee)
The purpose of this work and the project under which it was created is to develop, compare and validate several theoretical approaches and computation methods used to calculate the cross sections of dissociative recombination. For the most part it is con- cerned with the indirect dissociative recombination of molecular ions of H+ 2 in the singlet ungerade channels computed with three distinct approaches. First, the fully numerically solvable two-dimensional approach developed at ÚTF MFF UK as a part of my master's thesis. Second, a vibrational frame transformation method based on the work of Chang and Fano [E. S. Chang and U. Fano, Phys. Rev. A 6, 173 (1972)] and then enhanced into a full energy-dependent form by Gao and Greene [H. Gao and C. H. Greene, J. Chem. Phys. 91, 3988 (1989)], [H. Gao and C. H. Greene, Phys. Rev. A 42, 6946 (1990)], fur- ther improved by our own revisions. Third, a two-dimensional R-matrix method based on matching exact 2D solutions from a small interaction region to asymptotic solutions in the non-interacting region. We thoroughly discuss the various advantages and caveats of these methods and, in the later chapters, present our work on employing them for the realistic recombination of HeH+ + e− . Furthermore, we attempt to extend the presented models to the description of the...
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Two-dimensional model of dissociative recombination
Hvizdoš, Dávid ; Houfek, Karel (advisor)
The purpose of this thesis is to construct a numerically solvable quantum mechanical model describing the dynamics of the indirect mechanism of the dissociative recombination process of a molecular cation by electron impact. The model also describes vibrational excitation of a molecular cation by electron impact. The solution of this model is carried out by implementing a combination of finite elements, discrete variable representation and exterior complex scaling methods. This is then specifically applied to the dissociative recombination and vibrational excitation of H+ 2 by an incoming electron. The results can be used to test the accuracy of approximative methods and the programs expanded to cover the cases of other diatomics.
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Two-dimensional model of dissociative recombination
Hvizdoš, Dávid ; Houfek, Karel (advisor)
The purpose of this thesis is to construct a numerically solvable quantum mechanical model describing the dynamics of the indirect mechanism of the dissociative recombination process of a molecular cation by electron impact. The model also describes vibrational excitation of a molecular cation by electron impact. The solution of this model is carried out by implementing a combination of finite elements, discrete variable representation and exterior complex scaling methods. This is then specifically applied to the dissociative recombination and vibrational excitation of H+ 2 by an incoming electron. The results can be used to test the accuracy of approximative methods and the programs expanded to cover the cases of other diatomics.
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Two-dimensional model of dissociative recombination
Hvizdoš, Dávid ; Houfek, Karel (advisor) ; Čurík, Roman (referee)
The purpose of this thesis is to construct a numerically solvable quantum mechanical model describing the dynamics of the indirect mechanism of the dissociative recombination process of a molecular cation by electron impact. The model also describes vibrational excitation of a molecular cation by electron impact. The solution of this model is carried out by implementing a combination of finite elements, discrete variable representation and exterior complex scaling methods. This is then specifically applied to the dissociative recombination and vibrational excitation of H$_2^+$ by an incoming electron. The results can be used to test the accuracy of approximative methods and the programs expanded to cover the cases of other diatomics. Powered by TCPDF (www.tcpdf.org)
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Solution of integral equations for separable interactions
Hvizdoš, Dávid ; Horáček, Jiří (advisor) ; Kolorenč, Přemysl (referee)
Title: Solution of integral equations for separable interactions Author: Dávid Hvizdoš Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Jiří Horáček, DrSc., Institute of Theoretical Physics Abstract: This work deals with the most fundamental types of integral equations (Fredholm and Volterra). Their occurrence in quantum mechanics is illustrated and the process that leads to the so-called regular and Jost solution is presented. Further their solutions in the case of separable interactions are studied. Analytical solutions on model separable potentials are sought. Analytical extensions of these solutions to the complex energy plane are provided and the properties of these functions are examined. The method of analytical continuation in the coupling constant based on the extension of the coupling constant as a function of is introduced. For some examples of separable potentials the Taylor expansion of the function and from it the inverse series √ are calculated. These series are then used to determine the resonance parameters of the potential and the accuracy of these calculations is discussed. Key words: integral equations, scattering theory, resonances, separable potential
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