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Resonant state expansion for non-relativistic quantum mechanics in one dimension

Tanimu, Abdullahi 2018. Resonant state expansion for non-relativistic quantum mechanics in one dimension. PhD Thesis, Cardiff University.
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This thesis presents my work that I have done together with my supervisor, Dr Egor Muljarov. It is based on the resonant state expansion (RSE), a rigorous perturbation theory, recently developed in electrodynamics. Here, the RSE is applied to non-relativistic quantum mechanical systems in one dimension. To facilitate the analytics, the model of Dirac delta functions for describing quantum potentials was employed. The resonant states (RSs) of a symmetric double quantum well structure modeled by delta functions was first calculated. The full set of these RSs is investigated. This includes bound, anti-bound and normal resonant states which are all eigenstates solutions of Schrodingers equation with boundary conditions of outgoing waves. These RSs are then taken as an unperturbed basis state, for the quantum mechanical (QM) analogue of the RSE (QM-RSE). The transformation of the RSs and their transitions between different subgroups as well as the role of each subgroup in observables, such as the quantum transmission, is also analysed. The resonant state expansion is first verifed for a triple viii quantum well systems, showing convergence to the available analytic solution as the number of resonant states in the basis increases. The method is then applied to multiple quantum well and barrier structures, including finite periodic systems. Results are compared with the eigenstates in triple quantum wells and in- finite periodic potentials described by the famous Kronig-Penney model, revealing the nature of the resonant states in the studied systems.

Item Type: Thesis (PhD)
Date Type: Acceptance
Status: Unpublished
Schools: Physics and Astronomy
Subjects: Q Science > QC Physics
Funders: Umaru Musa Yar’adua University, Katsina
Date of First Compliant Deposit: 16 August 2018
Date of Acceptance: July 2018
Last Modified: 12 Oct 2018 15:19

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