Related papers: Two-Body Dirac Equation and Its Wave Function at t…
The model of Fermi particles with random two-body interaction is investigated. This model allows to study the origin and accuracy of statistical laws in few-body systems, the role of interaction and chaos in thermalization, Fermi-Dirac…
In this paper, we study the error bound between the Dirac--Fock ground-state energy and the Hartree--Fock ground-state energy, a quantity known as the relativistic effect in quantum mechanics. We confirm that the relativistic effect in the…
In this paper a one to one correspondence is established between space-time metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
We study two interacting quantum particles forming a bound state in $d$-dimensional free space, and constrain the particles in $k$ directions to $(0,\infty)^k \times \mathbb{R}^{d-k}$, with Neumann boundary conditions. First, we prove that…
The two-body Dirac equations for the bound q bar q systems are obtained from the different (five) versions of the 3D-equations derived from Bethe-Salpeter equation with the instantaneous kernel in the momentum space using the additional…
We study the properties of two quantum particles which are confined in a ring. The particles interact via a long-range gauge potential proportional to the distance between the particles. It is found that the two-body ground state…
Based on the Dirac approach we have developed the relativistic vision of the WKB method for centrally symmetrical potential with mixed Lorenz structure. We have obtained relativistic wavefunctions of light quark and the new rule of…
It is shown that a Dirac(-type) equation for a rank-two bi-spinor field on Minkowski (configuration) spacetime furnishes a Lorentz-covariant quantum-mechanical wave equation in position-space representation for a single free photon. This…
We revisit a recent discussion about the boundary condition at the origin in the Schroedinger radial equation for central potentials. Using a slight modification of the usual spherical coordinates, the origin of a previously reported Dirac…
By using symmetry properties, the two-body Dirac equation in coordinate representation is reduced to the coupled pair of radial second-order differential equations. Then the large-j expansion technique is used to solve a bound state…
This work aims to shed some light on the meaning of the positive energy assumption in relativistic quantum theory and its relation to questions of localization of quantum systems. It is shown that the positive energy property of solutions…
In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…
The kinematical formalism for describing spinning particles developped by the author is based upon the idea that an elementary particle is a physical system with no excited states. It can be annihilated by the interaction with its…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
These notes provide two derivations of the Lorentz-Dirac equation. The first is patterned after Landau and Lifshitz and is based on the observation that the half-retarded minus half-advanced potential is entirely responsible for the…
The light-front dynamics (LFD) of the scalar field model theory is analyzed to solve the two-body bound-state problem. The light-front two-body bound-state equation is extended to the full LFD kernel including the ladder, cross-ladder,…
We construct an infinite component relativistic wave equation which is a linear first order differential equation identical in form to a Dirac like equation, describing composite fields possessing multiple spin and energy states. The main…
The Weyl-Wigner-Moyal formalism for Dirac second class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this formalism, it is applied to the case of the…
A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and…