Related papers: Klein-Gordon equation for a particles in brane mod…
The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole…
In this paper, our focus is on investigating the impact of cosmological constant on relativistic quantum systems comprising spin-0 scalar particles. Our analysis centers around the Klein-Gordon equation, and we obtain both approximate and…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
With appropriate modifications, the multi-spin Klein-Gordon (KG) equation of quantum field theory can be adapted to curved spacetime for spins 0,1,1/2. The associated particles in the microworld then move as a wave at all spacetime…
We produce an explicit formula for the wave function of the spherically symmetric fields emitted to the FLRW universe with the scale factor generated by the de~Sitter universe. As an application of these explicitly written solutions of the…
The behavior of a quantum test particle satisfying the Klein-Gordon equation in a certain class of 4 dimensional stationary space-times is examined. In a space-time of a spinning cosmic string, the wave function of a particle in a box is…
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…
General classical equation of spin motion is explicitly derived for a particle with magnetic and electric dipole moments in electromagnetic fields. Equation describing the spin motion relatively the momentum direction in storage rings is…
We address the Klein-Gordon equation for a spinless charged particle in the presence of an electromagnetic (EM) field, and focus on its known shortcoming, related to the existence of solutions with a negative probability density. We…
In order to reduce the Klein-Gordon equation (with minimal coupling), we introduce a generalization of the so-called "mode solutions" that are well-known in the special case of a Robertson-Walker universe. After separation of the variables,…
The general classical equation of spin motion is rigorously derived for a particle with electric and magnetic charges and dipole moments in electromagnetic fields. The equation describing the spin motion relative to the momentum direction…
The Klein-Gordon and Dirac equations are considered in a semi-infinite lab ($x > 0$) in the presence of background metrics $ds^2 =u^2(x) \eta_{\mu\nu} dx^\mu dx^\nu$ and $ds^2=-dt^2+u^2(x)\eta_{ij}dx^i dx^j$ with $u(x)=e^{\pm gx}$. These…
A universal quantum wave equation that yields Dirac, Klein-Gordon, Schrodinger and quantum heat equations is derived. These equations are related by complex transformation of space, time and mass. The new symmetry exhibited by these…
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…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
Recently, finding exact solutions of nonlinear fractional differential equations has attracted great interest. In this paper, the space time-fractional Klein-Gordon equation with cubic nonlinearities is examined. Firstly, suitable exact…
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 Dirac equation, central to relativistic quantum mechanics, governs spin-$\frac{1}{2}$ particles and their antiparticles, with each spinor component satisfying the Klein-Gordon equation - the quantum counterpart of the relativistic mass…
We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic…
Classical dynamics of spinning zero-size objects in an external gravitational field is derived from the conservation law of the stress-energy and spin tensors. The resulting world line equations differ from those in the existing literature.…