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Doctor of Philosophy, (Mathematics)
Study Completed: 2014
College of Sciences
On Essential Self-adjointness,Confining Potentials & the Lp-Hardy Inequality
In layman’s terms, a Schrodinger (Sh–row-din–ger) operator is essentially self-adjoint if a particle under the influence of the associated potential is unable to come into contact with the boundary of a domain. The problem of determining the minimal criteria under which a Schrodinger operator is essentially self-adjoint can be phrased in terms of a balancing act between the quantum tunnelling effect and the uncertainty principle, the latter effect being given precise embodiment by the L2-Hardy inequality. It appears that the necessary and sufficient conditions required for a domain to admit this inequality depend intimately on the dimension of the boundary.
Distinguished Professor Gaven Martin
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Last updated on Tuesday 04 April 2017