相关论文: Regularization of a three-body problem with zero-r…
In this paper, we further investigate the planar Newtonian three-body problem with a focus on collinear configurations, where either the three bodies or their velocities are aligned. We provide an independent proof of Montgomery's result,…
The method of zero range potential (ZRP) for one-electron problems is reviewed. In the absence of an external electromagnetic field, the notion of a ZRP is introduced from different points of view and for an arbitrary dimension of space.…
In the low-energy limit, non-relativistic particles with short-range interactions exhibit universal behavior that is largely independent of microscopic details. This universality is typically described by effective field theory, in which…
We propose new effective inter-nucleon forces with a finite-range three-body operator. The proposed forces are suitable for describing the nuclear structure properties over a wide mass number region, including the saturation point of…
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be…
Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…
[This is an expository article. I have submitted it to the American Mathematical Monthly.] The three-body problem defines a dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes…
We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two $0^+$ levels in…
The zero-range potentials of the radial Schrodinger equation are investigated from a point of Darboux transformations scheme. The dressing procedure is realized as a sequence of Darboux transformations in a way similar to that used to…
We study Efimov physics for three identical bosons interacting via a pairwise square-well potential, analyze the validity of the separable approximation as a function of the interaction strength, and investigate what is needed to improve…
We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body systems consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation,…
We present an illustration of using a quantum three-body code being prepared for public release. The code is based on iterative solving of the three-dimensional Faddeev equations. The code is easy to use and allows users to perform…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
The three-body continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a Lippmann-Schwinger type equation, where the Green's function includes the leading…
A coordinate space approach, based on that used by Efimov, is applied to three-body systems with contact interactions between pairs of particles. In systems with nonzero orbital angular momentum or with asymmetric spatial wave functions,…
Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we renormalize the vacuum expectation value of the stress-energy tensor (and of the total energy) for a scalar field in presence of an…
We consider periodic and quasi-periodic solutions of the three-body problem with homogeneous potential from the point of view of the equivariant calculus of variations. First, we show that symmetry groups of the Lagrangian action functional…
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…
We discuss the impact of a finite effective range on three-body systems interacting through a large two-body scattering length. By employing a perturbative analysis in an effective field theory well suited to this scale hierarchy we find…
The bound state energies and wave functions for a particle exposed to the Hulth\'en potential field in the D-dimensional space are obtained within the improved quantization rule for any arbitrary l state. The present approximation scheme…