We review recent developments in the theory of 1-D Schrödinger operators with local point
interactions on a discrete set. The progress in this area was stimulated by recent advances …

We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an
attractive δ'-interaction, of strength β, centred at 0 (the bottom of the confining parabolic …

A zero-thickness limit for two-terminal and three-terminal devices from the quantum
electronics domain is analysed. The study is focused on heterostructures composed of a …

We investigate the ground states of the one-dimensional nonlinear Schr\" odinger equation
with a defect located at a fixed point. The nonlinearity is focusing and consists of a subcritical …

Abstract For real L_ ∞ (R)-functions Φ and Ψ of compact support, we prove the norm
resolvent convergence, as ε and ν tend to 0, of a family S_ ε ν of one-dimensional …

For a real-valued function V of the Faddeev–Marchenko class, we prove the norm-resolvent
convergence, as ε→ 0, of a family Sε of one-dimensional Schrödinger operators on the line …

For real functions\Phi and\Psi that are integrable and compactly supported, we prove the
norm resolvent convergence, as\epsilon\goes to 0, of a family S (\epsilon) of one …

Much of the literature on point interactions in quantum mechanics has focused on the
differential form of Schrödinger's equation. This paper, in contrast, investigates the integral …

We consider a compact metric graph of size ε and attach to it several edges (leads) of length
of order one (or of infinite length). As ε goes to zero, the graph G ε obtained in this way looks …

We develop an approach on how to define single-point interactions under the application of
external fields. The essential feature relies on an asymptotic method based on the one-point …