• Corpus ID: 56321886

Hamiltonians for systems of N particles interacting through point interactions

@article{DellAntonio1994HamiltoniansFS,
  title={Hamiltonians for systems of N particles interacting through point interactions},
  author={Gianfausto Dell'Antonio and Rodolfo Figari and Alessandro Teta},
  journal={Annales De L Institut Henri Poincare-physique Theorique},
  year={1994},
  volume={60},
  pages={253-290}
}
En utilisant des techniques de renormalisation de formes quadratiques singulieres, on etudie des Hamiltoniens pour systemes de N particules avec interactions de portee nulle, en dimension deux. Si on utilise la meme methode en dimension trois, on obtient des formes quadratiques qui, pour N = 3, ont une borne inferieure seulement si l'on impose des conditions de symetrie, et qui, pour N assez grand, n'ont, en tout cas, pas de borne inferieure 
numdam.org
95 Citations
Highly Influential Citations
15
Background Citations
39
Methods Citations
12
Results Citations
3

95 Citations

ON POINT INTERACTIONS REALISED AS

For quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultraviolet asymptotics known as…

On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians

A Nonrelativistic Quantum Field Theory with Point Interactions in Three Dimensions

We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles,…

On Point-Like Interaction between n Fermions and Another Particle

In this note the point-like interaction of n fermions with a particle of a different nature is considered in a framework of the theory of self-adjoint extensions of symmetric operators. It introduces…

From Short-Range to Contact Interactions in the 1d Bose Gas

For a system of N bosons in one space dimension with two-body δ -interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian…

From Short-Range to Contact Interactions in the 1d Bose Gas

For a system of N bosons in one space dimension with two-body δ-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian…

On Nelson-Type Hamiltonians and Abstract Boundary Conditions

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation…

On Nelson-Type Hamiltonians and Abstract Boundary Conditions

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation…

Multi-particle Schrödinger operators with point interactions in the plane

We study a system of N-bosons in the plane interacting with delta function potentials. After a coupling constant renormalization we show that the Hamiltonian defines a self-adjoint operator and…

Finiteness of the discrete spectrum in a three-body system with point interaction

Abstract In this paper we are concerned with a three-body system with point interaction, which is called the Ter-Martirosian–Skornyakov extension. We locate the bottom of the essential spectrum of…
...

20 References

ON THE THEORY OF THE DISCRETE SPECTRUM OF THE THREE-PARTICLE SCHRÖDINGER OPERATOR

We investigate the discrete spectrum of the Schr?dinger operator H for a system of three particles. We assume that the operators h?, ? = 1,?2,?3, which describe the three subsystems of two particles…

On the finiteness of the discrete spectrum of Hamiltonians for quantum systems of three one- or two-dimensional particles

The system of three particles (acting in K dimensions (K=1, 2)) without stable two-particle subsystems is studied. For short-range potentials Vij(rij), the finiteness of the discrete spectrum is…

Annales de l'Institut Henri Poincaré

  • H. P.
  • Mathematics
    Nature
  • 1931
The first number of the Annales was noticed in Nature of Oct. 11, 1930 (p. 564). In the second number we have de Donder on Einstein's theory of gravitation, Pólya on some points in the theory of…

Binding of three identical bosons in two dimensions

Qualitative features are discussed for the binding of three identical bosons interacting through pair potentials in two dimensions. Two special cases, known to yield pathologies in three dimensions,…

A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior

THREE BODY PROBLEM FOR SHORT RANGE FORCES. I. SCATTERING OF LOW ENERGY NEUTRONS BY DEUTERONS

An exact solution is obtained for the three body problem in the limiting case of a vanishingly small radius of action of the forces. In this case, the Schrodinger equation for the system of three…

The non-relativistic limit ofP(ϕ)2 quantum field theories: Two-particle phenomena

It is proved that for two-particle phenomena theP(ϕ)2 quantum field theories with speed of lightc converge to non-relativistic quantum mechanics with a δ function potential in the limitc→∞.

Solvable models in quantum mechanics

Name: Helge Holden, Born: September 28, 1956 in Oslo. Norwegian nationality Position: Professor of mathematics Address: Department of Mathematical Sciences, NTNU Norwegian University of Science and…

Quadratic forms for singular perturbations of the Laplacian

Singular perturbations of -Δ in L 2 (R 3 ) supported by points, regular curves an regular surfaces are considered. Using a renormalization technique the corresponding quadratic forms are constructed…

The Interaction Between a Neutron and a Proton and the Structure of H**3