Analýza srážkových procesů v kvantové mechanice s použitím Siegertových stavů
| Název práce v češtině: | Analýza srážkových procesů v kvantové mechanice s použitím Siegertových stavů |
|---|---|
| Název v anglickém jazyce: | Analysis of collision processes in quantum mechanics using Siegert states |
| Klíčová slova: | teorie rozptylu|S-matice|teorie R-matic|resonance|virtuální stavy |
| Klíčová slova anglicky: | Scattering theory|S-matrix|R-matrix theory|resonance|virtual state |
| Akademický rok vypsání: | 2020/2021 |
| Typ práce: | bakalářská práce |
| Jazyk práce: | čeština |
| Ústav: | Ústav teoretické fyziky (32-UTF) |
| Vedoucí / školitel: | Mgr. Zdeněk Mašín, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 08.10.2020 |
| Datum zadání: | 15.10.2020 |
| Datum potvrzení stud. oddělením: | 30.12.2020 |
| Datum a čas obhajoby: | 08.07.2021 09:00 |
| Datum odevzdání elektronické podoby: | 27.05.2021 |
| Datum odevzdání tištěné podoby: | 27.06.2021 |
| Datum proběhlé obhajoby: | 08.07.2021 |
| Oponenti: | doc. RNDr. Karel Houfek, Ph.D. |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| 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). |
| Předběžná náplň práce v anglickém jazyce |
| 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. |