Finitely many δ interactions with supports on concentric spheres

Abstract

Using the theory of self-adjoint extensions of symmetric operators the precise mathematical definition of the quantum Hamiltonian describing a finite number of δ interactions with supports on concentric spheres is given. Its resolvent is also derived, its spectral properties are described, and it is shown how this Hamiltonian can be obtained as a norm resolvent limit of a family of local scaled short-range Hamiltonians.