Point Interaction Hamiltonians in Bounded Domains

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.

18 pages, 3 figures, latex

References in corpus (7)

• Star graphs and Seba billiards
• Resolvents of self-adjoint extensions with mixed boundary conditions
• Point interactions in a strip
• A remark on Krein's resolvent formula and boundary conditions
• Quantum mechanics of layers with a finite number of point perturbations
• Spin dependent point potentials in one and three dimensions
• Point perturbations of circle billiards

Cited by in corpus (5)

• On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions
• Correctness of the definition of the Laplace operator with delta-like potentials
• On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region
• Faber-Krahn inequalities for Schrödinger operators with point and with Coulomb interactions
• Resonances and resonance expansions for point interactions on the half-space