Self-adjoint Extensions Of Symmetric Operators Research Articles

Finitely many δ interactions with supports on concentric spheres

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.

Theory of the self-adjoint extensions of symmetric operators with a spectral gap

Theory of the self-adjoint extensions of symmetric operators with a spectral gap

Self-adjoint extensions of symmetric operators

Let ℋ denote the Hilbert space of analytic functions on the unit disk which are square summable with respect to the usual area measure. In this paper we consider the formal differential exepressons of order two or greater having the form {fx321-1} and {fx321-2} which give rise to symmetric operators in ℋ. We show that these operators in ℋ admit self-adjoint extensions in ℋ.