The δ point interaction two‐center system

Abstract

ABSTRACT:Motivated by the behavior of molecules in strong magnetic fields, we study the quantum system consisting of a particle (electron) interacting with two fixed (nuclear) centers by δ-type point interactions. Spectral properties and resonances of this model as a function of the internuclear separation are investigated qualitatively and quantitatively. We prove analyticity, monotonicity, and other features, compare them with corresponding attributes of related Coulomb systems, and point out the consequences for molecules.

On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

“…If R(z) denotes the full resolvent operator (H κ,σ − z) −1 and R 0 (z) denotes the resolvent (H 0,σ − z) −1 , then by Krein's formula 3 and its entries are z dependent. We will denote the elements of τ R 0 (z)τ * by…”

“…The framework described in Section 3 is easily generalized to the operator H κ,κ . Consequently, E < −κ 2 /2 is a discrete eigenvalue of H κ,κ if and only if the inverse of the operator G κ,κ (E) does not exist on [L 2 (R)] 3 , where G κ,κ (E) is given by…”

“…The bound states of a helium like system with two negatively charged particles and a positively charged nucleus interaction through zero range potentials were previously examined in [1] and in [2], while the bound states of a system with a negatively charged particle and two positively charged particles with infinite mass were examined in [3]. Also, the spectral properties of the similar, but more realistic, three-body Coulomb systems in three dimensions have been examined in [4,5,6].…”

An electron in the presence of multiple zero range potentials and an external laser field -- exact solutions for photoionization and stimulated bremsstrahlung

“…Regarding current status of the usage of the method of ZRP to model molecular systems see, e.g., Refs. [50].…”

Redox processes at a nanostructured interface under strong electric fields

“…4b. Moreover we utilize a minimal representation of active electrons, replace the electron/nucleus attractive Coulomb potentials with Dirac delta-functions 38 (see ESI † 25 ), and solve the problem in one-dimension (the x-axis) which is the direction of electron scattering, see Fig. 4c.…”