National Repository of Grey Literature 15 records found  previous11 - 15  jump to record: Search took 0.01 seconds. 
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
Analysis of the Stieltjes imaging method for the calculation of resonance widths
Votavová, Petra ; Kolorenč, Přemysl (advisor) ; Čížek, Martin (referee)
Title: Analysis of the Stieltjes imaging method for the calculation of resonance widths Author: Petra Votavová Department: Institute of Theoretical Physics Supervisor: RNDr. Přemysl Kolorenč, Ph.D., Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague Abstract: This thesis deals with the moment problem in the context of the resonance widths. The moment problem was solved by the Stieltjes imaging method and proposed alternative method based on the direct decomposition into the orthogonal basis. Three different basis derived from the Legendre polynomials were chosen. The properties of these methods were studied by analytical function. Eventually, both methods were applied to the calculation of resonance width of the metastable ion CH3F(2s-2 )2+ . Keywords: moment problem, Gaussian quadrature, orthogonal polynomials, resonance widths, decay of metastable ions
Multimode vibrational dynamics of electron scattering from molecule
Táborský, Jiří ; Čížek, Martin (advisor) ; Kolorenč, Přemysl (referee)
In the present work we study vibrational excitation of a generally polyatomic molecule by electron impact. We proceed from the theory of discrete state in continuum and the nonlocal resonance model and we approximate the molecule using two-dimensional harmonic oscillator. We have written numerical procedures in Fortran which compute a cross section of these collisions. The correctness of a transition from 1D model to 2D has been verified. We have performed several computations using different initial parameters and have studied the effect of changing selected parameters on the cross section depending on the energy of the incoming electron. Powered by TCPDF (www.tcpdf.org)
Rezonanční srážky elektronů s molekulami
Formánek, Martin ; Houfek, Karel (advisor) ; Kolorenč, Přemysl (referee)
In the present work we study different approaches for solving the nuclear dy- namics of resonant electron molecule collisions. Namely, we review two methods addressing this phenomenon which are a local complex potential (LCP) approxi- mation and a nonlocal resonance model (NRM). We briefly discuss a numerical implementation of these methods. We show how to derive model parameters for both of them from fixed-nuclei scattering calculations and we implement them in the time independent picture of quantum mechanics. We compare their vibrational excitation cross sections for the diatomic molecule CO. Then we generalize the non- local resonance model for systems with more nuclear degrees of freedom. Output of our work is a computer code producing the vibrational excitation cross sections for systems with two degrees of freedom. We aim to use this code for studying a threshold behavior of the low-energy electron collisions with the CO2 molecule and therefore we review a current state of understanding for this phenomenon. Mea- nwhile we test the functionality of the code by comparing results with those of the LCP approximation on a simple 2D model system.
Study of resonance and threshold effects on simple two-channel model
Kocák, Jakub ; Čížek, Martin (advisor) ; Kolorenč, Přemysl (referee)
In this thesis we study simple one-dimensional two-channel scattering model where pointlike coupling between channels is provided by the delta potential. The scattering task can be completely solved analytically. The solution of the Lippmann-Schwinger equation leads to improper scattering eigenvectors, consequently to scattering S matrix elements and eigenphases. We study how the setting of parameters affects threshold and resonant behaviour (presence, position, width) and the mutual relationship between resonances and poles of the S matrix in complex k-plane. Then we apply projection- operator formalism to model with resonance and the on-shell T matrix is separated into the orthogonal, direct and resonant term. We discuss how choice of subspace of quasi-bound states effects the separation. Powered by TCPDF (www.tcpdf.org)

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