Next to the harmonic oscillator and the Coulomb potential the class of two-body models with
point interactions is the only one where complete solutions are available. All mathematical …

For a system of spinless one-dimensional fermions, the nonvanishing short-range limit of a
two-body interaction is shown to induce the wave-function discontinuity. We prove the …

Investigation of the differential operators with the generalized coefficients having singular
support on a disjoint set of points requires the consideration of the distribution theory with …

This article is a direct illustration of a construction of coherent states which has been recently
proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in …

We show that the most general three-parameter family of point interactions on the line can
be expressed as the self-adjoint local operators in terms of three Dirac's delta functions with …

We discuss the existence and the physical properties of the one-dimensional δ′-interaction
Hamiltonian. We show that the so called δ′-interaction Hamiltonian which appears in the …

Spectral properties of 1-D Schrödinger operators [Formula: see text] with local point
interactions on a discrete set [Formula: see text] are well studied when d∗:= infn, k∈ N| xn …

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 …

The generalized point interaction in one dimension Page 1 THE GENERALIZED POINT
INTERACTION IN ONE DIMENSION P. ~eba Nuclear Centre, Faculty of Mathematics and …

The transformations of all the Schrödinger operators with point interactions in dimension one
under space reflection P, time reversal T and (Weyl) scaling W λ are presented. In particular …