Related papers: A five-dimensional perspective on the Klein-Gordon…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…
The positivity of the energy in relativistic quantum mechanics implies that wave functions can be continued analytically to the forward tube T in complex spacetime. For Klein-Gordon particles, we interpret T as an extended (8D) classical…
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 fact that the probability density expression provided by the Klein-Gordon equation can take on negative values is usually seen as an obstacle to formulating a particle interpretation of quantum mechanics. Nevertheless, reconciling this…
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 possible way for the consistent probability interpretation of the Klein-Gordon equation is proposed. It is assumed that some states of a scalar charged particle cannot be physically realized. The rest of quantum states are proven to have…
In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results…
We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle and antiparticle wave function components with positive probability densities.…
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…
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…
A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Pe\~na and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to…
We study the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity paramete and by comparing to the 2S - 1S…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
We define a modified covariant Klein-Gordon (KG) equation containing quantum vacuum contributions arising from the self-interaction of matter with its own internal kinetic energy. The modified KG equation is exemplified for a variety of…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution.…
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…
The implications of manifestly covariant formulation of relativistic quantum mechanics depending on a scalar evolution parameter, canonically conjugated to the variable mass, is still an unsettled issue. In this work we find a complete set…