ﻻ يوجد ملخص باللغة العربية
We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $delta$-$delta$ interaction. After a simple general presentation in one dimension, we briefly discuss a one dimensional periodic potential with a $delta$-$delta$ interaction at each node. The dependence of energy bands with the parameters (coefficients of the deltas) can be computed numerically. We also study the $delta$-$delta$ interaction supported on spheres of arbitrary dimension. The spherical symmetry of this model allows us to obtain rigorous conclusions concerning the number of bound states in terms of the parameters and the dimension. Finally, a $delta$-$delta$ interaction is used to approximate a potential of wide use in nuclear physics, and estimate the total number of bound states as well as the behaviour of some resonance poles with the lowest energy.
We first review the problem of a rigorous justification of Kubos formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on t
The spherically symmetric potential $a ,delta (r-r_0)+b,delta (r-r_0)$ is generalised for the $d$-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac delta, the spectrum
Based on a method that produces the solutions to the Schrodinger equations of partner potentials, we give two conditionally exactly solvable partner potentials of exponential type defined on the half line. These potentials are multiplicative shape in
We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape invariant. The m
We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S^d in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz p