We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example, we get solutions that mimic the Harmonic oscillator energy levels, surprisingly. An equation similar to the beam equation is obtained in the process.

The Green function for Klein-Gordon-Dirac equation is obtained. The case with the dominating Klein-Gordon term is considered. There seems to be a formal analogy between our problem and a certain problem for a 4-dimensional particle moving in the external field. The explicit relations between the wave function, Green function and initial conditions are established with the help of the T -exponen...

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential V (r) is established. It is shown that Nmπ = π (nm − n−m) = [δm(M) + β1]− [δm(−M) + β2] ,where Nm denotes the difference between the number of bound states of the particle nm and the ones of antiparticle n−m with a fixed angular momentum m, and the δm is named phase shifts. The constants ...

For free Klein-Gordon fields, we construct a one-parameter family of conserved current densities J a , with a ∈ (−1, 1), and use the latter to yield a manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. Employing a recently developed method of constructing the Hilbert space and observa...

We construct small amplitude breathers in 1D and 2D Klein–Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schrödinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schrödinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum...

The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the noncentral equal scalar and vector potentials. The results obtained in this work are m...

Solving Nonlinear Klein-Gordon Equation with a Quadratic Nonlinear term using Homotopy Analysis Method H. Jafari , M. Saeidy, M. Arab Firoozjaee Department of Mathematics and Computer Science, University of Mazandaran, P. O. Box 47416-1467, Babolsar, Iran. Abstract In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy...

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considere...