相关论文: Klein paradox and antiparticle

We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies…

This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…

Recently the interest in relativistic quantum plasma is increasing primarily to understand the fundamentals of the plasma behaviour and its properties. Mathematical models used to investigate these plasma are still need to be matured.…

The Collins mechanism provides a non-perturbative explanation for the large single spin asymmetries found in hard semi-inclusive reactions involving a transversely polarized nucleon. However, there are seemingly convincing reasons to…

We introduce an embedding of the Klein-Gordon equation into a pair of coupled equations that are first-order in time. The existence of such an embedding is based on a positivity property exhibited by the Klein-Gordon equation. These coupled…

By recasting the Klein--Gordon equation as an eigen-equation in the coupling parameter $v > 0,$ the basic Klein--Gordon comparison theorem may be written $f_1\leq f_2\implies G_1(E)\leq G_2(E)$, where $f_1$ and $f_2$, are the monotone…

We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein-Gordon equation with a variable coefficient. Using the…

We consider a system of two coupled non-linear Klein-Gordon equations. We show the existence of standing waves solutions and the existence of a Lyapunov function for the ground state.

We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on $\bf R^N$, for $1\leq N\leq…

The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the…

We show that the Klein-Gordon equation on the quaternion field is equivalent to a pair of DKP equations. We shall also prove that this pair of DKP equations can be taken back to a pair of new KG equations. We shall emphasize the important…

Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…

The Dirac equation requires a treatment of the step potential that differs fundamentally from the traditional treatment, because the Dirac plane waves, besides momentum and spin, are characterized by a quantum number with the physical…

The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein…

We consider Klein-Gordon equations with an external potential $V$ and a quadratic nonlinearity in $3+1$ space dimensions. We assume that $V$ is regular and decaying and that the (massive) Schr\"odinger operator $H=-\Delta+V+m^2$ has a…

We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in…

Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…

EPR experiment on $K^0-\bar{K}^0$ system in 1998\cite{1} strongly hints that one should use operators $\hat{E}_c=-i\hbar\frac{\partial}{\partial t}$ and $\hat{\bf p}_c=i\hbar\nabla$ for the wavefunction (WF) of antiparticle. Further…

In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…

In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and…