Thesis-2004-Sayles.pdf (813.91 kB)
Integrable Schroedinger operators with magnetic fields
thesisposted on 2018-09-11, 09:22 authored by Matthew R.J. Sayles
We consider the problem of classifying all pairs of commuting Schrodinger operators with magnetic terms in two degrees of freedom. We derive a concise set of necessary and sufficient conditions for two such operators to commute, and identify the difference compared with the corresponding conditions in the classical case. We classify all such pairs of operators in the case when one of them has a constant, non-zero magnetic field and a non-constant potential.
Engineering and Physical Sciences Research Council.
- Mathematical Sciences
Publisher© Matthew Sayles
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesA Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.