In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

The inverse scattering problem on branching graphs is studied. The definition of the
Schrödinger operator on such graphs is discussed. The operator is defined with real …

We show that a one-dimensional Schrödinger equation in which the potential is a delta well
plus a δ′ interaction at the same point has a bound state, and we obtain the energy of this …

The quantum dynamics of a free particle on a circle with point interaction is described by a U
(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing …

The scattering properties of regularizing finite-range potentials constructed in the form of
squeezed rectangles, which approximate the first and second derivatives of the Dirac delta …

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 …

We study a one-dimensional singular potential plus two types of regular interactions:
constant electric field and harmonic oscillator. In order to search for the bound state …

In one-dimensional quantum gases there is a well known “duality” between hard core
bosons and noninteracting fermions. However, at the field theory level, no exact duality …

General point interactions for the second derivative operator in one dimension are studied.
In particular, P T-self-adjoint point interactions with the support at the origin and at points±l …