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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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Particle interaction with atoms in optical lattice
Vozáb, Filip ; Čížek, Martin (advisor) ; Kolorenč, Přemysl (referee)
The thesis discusses description of associative detachment of electron in the iont interaction with neutral atoms in optical lattice. This is given by combination of the model for interaction of particles in optical lattice, given by periodic potential, and of the model for associative detachment of electron, describe by imaginary component of the potential. In thesis is stated form of Schrödinger's equation for periodic potential, and subsequent solution of such equation in case of general complex and non hermitian Hamiltonian (because of imaginary component of potential). I specifically compute complex energetic levels one-dimensional model with numeric method from software package EISPACK for non hermitian Hamiltonian decomposed into finite base. 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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