It is proved that no Hamiltonian exists for the real Klein-Gordon field used in the Yukawa interaction. It is also shown that a real Klein-Gordon particle can be neither in a free isolated state nor in a bound state having an angular momentum l > 0. The experimental data support these conclusions. This outcome is in a complete agreement with Dirac's negative opinion on the Klein-Gordon equation.

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 ...