Scholtens, Robbert (2022) A Transparent View on Resonances. Master's Thesis / Essay, Mathematics.
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Abstract
This thesis concerns itself with resonances as arising from 1D scattering experiments in quantum systems, and explores their relation to transparencies. An introduction is given to (the interpretation of) complex energies, and the resolvent operator—whose poles are by definition resonances—is defined. Resonances are then redefined as poles of the transmission amplitude S(k), and some further properties of S(k) are proven. Explicit formulae for S(k) are obtained for i) symmetric piecewise-constant potentials, and ii) symmetric potentials for which WKB may be applied. The latter shows that Bohr-Sommerfeld quantization plays a role despite the exclusion of bound states. Finally, quantum normal forms (QNFs) are discussed, which describe S(k) when the energy is approximately that of a local maximum of the potential. This may bridge the gap between energy various energy regions in which WKB is applicable.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Waalkens, H. and Boer, D. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 21 Jul 2022 06:06 |
| Last Modified: | 21 Jul 2022 06:06 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/28055 |
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