Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.778739 |
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Title: | Geometrical dynamics by the Schrödinger equation and coherent states transform | ||||||
Author: | Almalki, Fadhel Mohammed H. |
ISNI:
0000 0004 7964 4676
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Awarding Body: | University of Leeds | ||||||
Current Institution: | University of Leeds | ||||||
Date of Award: | 2019 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
This thesis is concerned with a concept of geometrising time evolution of quantum systems. This concept is inspired by the fact that the Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider, in this thesis, coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to first-order partial differential operators. Therefore, the respective dynamics can be explicitly solved through a flow of points in extensions of the phase space. This, in particular, generalises the geometric dynamics of a harmonic oscillator in the Fock-Segal-Bargmann (FSB) space. We describe all Hamiltonians which are geometrised (in the above sense) by Gaussian and Airy beams and exhibit explicit solutions for such systems.
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Supervisor: | Kisil, Vladimir V. | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.778739 | DOI: | Not available | ||||
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