Point Interaction Hamiltonians in Bounded Domains
Mathematical Physics
2009-11-13 v2 math.MP
Spectral Theory
Abstract
Making use of recent techniques in the theory of selfadjoint extensions of symmetric operators, we characterize the class of point interaction Hamiltonians in a 3-D bounded domain with regular boundary. In the particular case of one point interaction acting in the center of a ball, we obtain an explicit representation of the point spectrum of the operator togheter with the corresponding related eigenfunctions. These operators are used to build up a model-system where the dynamics of a quantum particle depends on the state of a quantum bit.
Keywords
Cite
@article{arxiv.0704.3249,
title = {Point Interaction Hamiltonians in Bounded Domains},
author = {Ph. Blanchard and R. Figari and A. Mantile},
journal= {arXiv preprint arXiv:0704.3249},
year = {2009}
}