White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Geometrical Dynamics by the Schrödinger Equation and Coherent States Transform

Almalki, Fadhel Mohammed H (2019) Geometrical Dynamics by the Schrödinger Equation and Coherent States Transform. PhD thesis, University of Leeds.

[img]
Preview
Text
Almalki_FMH_Mathematics_PhD_2019.pdf - Final eThesis - complete (pdf)
Available under License Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales.

Download (847Kb) | Preview

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

Item Type: Thesis (PhD)
Keywords: Harmonic oscillator, Schrödinger equation, coherent states, geometrical quantum dynamics
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Identification Number/EthosID: uk.bl.ethos.778739
Depositing User: mr Fadhel Almalki
Date Deposited: 09 Jul 2019 10:19
Last Modified: 18 Feb 2020 12:50
URI: http://etheses.whiterose.ac.uk/id/eprint/24386

You do not need to contact us to get a copy of this thesis. Please use the 'Download' link(s) above to get a copy.
You can contact us about this thesis. If you need to make a general enquiry, please see the Contact us page.

Actions (repository staff only: login required)