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Analýza srážkových procesů v kvantové mechanice s použitím Siegertových stavů
Thesis title in Czech: Analýza srážkových procesů v kvantové mechanice s použitím Siegertových stavů
Thesis title in English: Analysis of collision processes in quantum mechanics using Siegert states
Key words: teorie rozptylu|S-matice|teorie R-matic|resonance|virtuální stavy
English key words: Scattering theory|S-matrix|R-matrix theory|resonance|virtual state
Academic year of topic announcement: 2020/2021
Type of assignment: Bachelor's thesis
Thesis language: čeština
Department: Institute of Theoretical Physics (32-UTF)
Supervisor: Mgr. Zdeněk Mašín, Ph.D.
Author: hidden - assigned and confirmed by the Study Dept.
Date of registration: 08.10.2020
Date of assignment: 15.10.2020
Confirmed by Study dept. on: 30.12.2020
Date and time of defence: 08.07.2021 09:00
Date of electronic submission:27.05.2021
Date of submission of printed version:27.06.2021
Date of proceeded defence: 08.07.2021
Reviewers: doc. RNDr. Karel Houfek, Ph.D.
Familiarization with the basic theory of single- and multi-channel scattering in non-relativistic quantum mechanics. Derive analytic solutions for the Siegert states in simple two-channel systems. Implement a numerical method for finding the Siegert solutions of the Schrodinger equation. Study trajectories of the corresponding S-matrix poles on the Riemann surface of the S-matrix.
R.G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (1982).
V.I. Kukulin, V.M. Krasnopolsky, J.Horáček, Theory of resonances: principles and applications, (1989).
L.A. Morgan and P.G. Burke, J. Phys. B: At. Mol. Opt. Phys. 21, 2091 (1988).
Preliminary scope of work in English
In quantum mechanics of collision processes the basic quantity that is obtained in experiments is the scattering cross section which is a measure of the strength of interaction between the incoming particle and the target. The scattering cross section depends on the energy of the incoming particle and can have a complicated shape depending on the processes that take place during the collision.

For example the process of electron-atom collision can be strongly influenced by formation of so called virtual and resonant states of the electron during the collision. However, an unambiguous identification of these states may be difficult especially in collisions where more channels (such as electronic excitation of the atom) are open. The resonant and virtual states are special cases of so called Siegert states which are solutions of the Schrodinger for complex momenta (energies).

In this work we will focus on development of analytic and numerical methods for direct computation of the Siegert states in simple models of quantum mechanical systems. This work will result in the development of a general methodology for a detailed analysis of computed scattering cross sections. This work can be extended by implementation of this approach into sophisticated ab initio codes for studying electron collisions with atoms and molecules.
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