Related papers: Non-locality and time-dependent boundary condition…
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…
In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein-Gordon and Dirac equations in Rindler coordinates with…
The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…
In this paper we present two different classes of solutions for the Klein-Gordon equation in the presence of a scalar potential under the influence of noninertial effects in the cosmic string spacetime. We show that noninertial effects…
We discuss the non-relativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, highlighting and clarifying several subtleties. We study the following topics: (a)…
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…
We illustrate, using a simple model, that in the usual formulation the time-component of the Klein-Gordon current is not generally positive definite even if one restricts allowed solutions to those with positive frequencies. Since in de…
The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a ''particle'', which is both passively affected by, and actively affecting, a diffusion process of its…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or…
We derive an exact analytic solution to a Klein-Gordon equation for a step potential barrier with cutoff plane wave initial conditions, in order to explore wave evolution in a classical forbidden region. We find that the relativistic…
Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast,…
We study the non relativistic limit of the solutions of the cubic nonlinear Klein--Gordon (KG) equation with periodic boundary conditions on an interval and we construct a family of time quasi periodic solutions which, after a Gauge…
The standard theory of relativity is based on the hypothesis of locality. The locality principle assumes that an object is affected only by its immediate surroundings and not by variables in the past. It follows that in standard relativity…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.
We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of…
When applied to some models of noncommutative geometry, the formalism of relative locality predicts the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter,…
We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schr\"odinger equation (SE) violates local causality by causing instantaneous changes in the…