We present the mathematical construction of the physically relevant quantum Hamiltonians
for a three-body system consisting of identical bosons mutually coupled by a two-body …

We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-
Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely …

We study a class of two-dimensional nonlinear Schrödinger equations with point-like
singular perturbation and Hartree non-linearity. The point-like singular perturbation of the …

The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a
regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators …

We qualify the main features of the spectrum of the Hamiltonian of point interaction for a
three-dimensional quantum system consisting of three point-like particles, two identical …

A class of models is considered for a quantum particle constrained on degenerate
Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the …

In this first chapter of 'modern applications' we analyse the self-adjoint realisations of
hydrogenoid Hamiltonians with central, point-like perturbation and their spectral properties …

The problem of connecting the operator parameters that label the same self-adjoint
extension of a given symmetric operator, respectively, within the'absolute'von Neumann …

We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional
Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger …

We study the existence and the properties of ground states at fixed mass for a focusing
nonlinear Schrödinger equation in dimension two with a point interaction, an attractive …