The linear and non-linear Klein-Gordon equations are considered. fractional complex transform is used to convert the on a continuous space/time fractals ones Cantor sets, resultant solved by local reduced differential method. Three examples given show effectiveness of technology.

Abstract All causal Lie products of solutions the Klein-Gordon equation and wave in Minkowski space are determined. The results shed light on origin algebraic structures underlying quantum field theory.

Klein–Gordon equation with pseudoharmonic oscillator has been corrected through physical acceptable solutions. In a way, we correct the energy spectra related to its behavior versus potential parameter D e .

In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by eitφ( √ −∆), where φ : R+ → R is smooth away from the origin. Especially, the decay estimates for the solutions of the Klein-Gordon equation and the beam equation are simplified and slightly improved.

We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the field's polarization direction as well as in the transverse directions is re...

Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle described by either the Dirac equation or the Klein-Gordon equation because such a particle cannot be localized in the sense required by the theorems.

ABSTRACT : Quaternion Dirac equation has been obtained from the square root of Klein-Gordon equation in compact and consistent way. Dirac matrices are described as quaternion valued and the Dirac Hamiltonian is considered as Hermitian with real eigenvalues of energy. Dirac spinors and free particle energy solution has been obtained in terms of one component, two-component and four-component Dir...

The Klein-Gordon equation of the hydrogen atom has a low-lying eigenstate, called hydrino state, with square integrable wavefunction. The corresponding spinor solution of Dirac’s equation is not square integrable. For this reason the hydrino state has been rejected in the early days of quantum mechanics as being unphysical. Maybe it is time to change opinion.

Pointing out the difference between the Discrete Nonlinear Schrödinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the initial data and the dimension of the lattice-we prove either global existence or nonexistence in time, for the Discrete Klein-Gordon equation with the same type...

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon h̄-expansions and suitable quantization conditions a new procedure for deriving ...