Point interaction Hamiltonians in bounded domains

Blanchard P, Figari R, Mantile A. Point interaction Hamiltonians in bounded domains. JOURNAL OF MATHEMATICAL PHYSICS. 2007;48(8):082108.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