PUB - Publikationen an der Universität Bielefeld

Making use of recent techniques in the theory of self-adjoint extensions of symmetric operators, we characterize the class of point interaction Hamiltonians in a three-dimensional bounded domain with regular boundaries. 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 together with the corresponding 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.