Related papers: Generalized One-Dimensional Point Interaction in R…
Several families of one-point interactions are derived from the system consisting of two and three $\delta$-potentials which are regularized by piecewise constant functions. In physical terms such an approximating system represents two or…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to…
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a…
In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
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, which are bosons. The interaction…
An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…
The multirank separable kernels of the neutron-proton interaction for uncoupled $S$ and $P$ partial waves (with the total angular momentum $J$=0,1) are proposed. Two different methods of a relativistic generalization of initially…
The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
In this paper, we have applied a three-dimensional approach for calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is…
The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a…
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these…
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the…
Non-relativistic reduction of the S-matrix for the quasifree electron scattering process $A\left(~e, e'p~\right)A-1$ is studied in order to understand the source of differences between non-relativistic and relativistic models. We perform an…
We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed.…