Adam Ward

Citation

Thesis Title
On Essential Self-adjointness,Confining Potentials & the Lp-Hardy Inequality

Read article at Massey Research Online:

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.

Supervisors
Distinguished Professor Gaven Martin