Related papers: From Short-Range to Contact Interactions in Two-di…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to…
Solutions of the Schr\"odinger equation by spanning the wave function is a complete basis is a common practice is many-body interacting systems. We shall study the case of a two-dimensional quantum system composed by two interacting…
We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special…
We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schr\"odinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The…
Strongly interacting systems appear in several areas of physics and are characterized by attractive interactions that can almost, or just barely, loosely bind two particles. Although this definition is made at the two-body level, this gives…
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range,…
Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems,…
Symmetry classification of two-body central potentials in a two-particle Schr\"{o}dinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four…
The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several…
We introduce a new approach to analyzing the interaction between classical and quantum systems that is based on a limiting procedure applied to multi-particle Schr\"{o}dinger equations. The limit equations obtained by this procedure, which…
We prove that the Schr\"odinger operator describing four particles in two dimensions, interacting solely through short-range three-body forces, can possess infinitely many bound states. This holds under the assumption that each three-body…
Contact interaction is a fundamental concept that appears in various areas of physics. It simplifies physical models by replacing the detailed short-range interaction with a zero-range contact potential which reproduces the same low-energy…
We present examples of many-body Wigner quantum systems. The position and the momentum operators ${\bf R}_A$ and ${\bf P}_A,\; A=1,\ldots,n+1$, of the particles are noncanonical and are chosen so that the Heisenberg and the Hamiltonian…
In this paper, we present the exact solution to a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential $s(s+1)/{\rm sinh}^{2}(r)$, while unlike particles interact with a pair…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably…
The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^\gamma$. It is shown that $\gamma$ is quantitatively related to…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…