An analytical solution of the Klein–Fock–Gordon equation for a 2D pion atom moving in a constant uniform magnetic field

The Klein–Fock–Gordon equation is solved for a 2D pion moving in a constant uniform magnetic field. A relativistic energy spectrum is calculated for fixed values of the angular momentum and magnetic field Н. An analysis of the results of these calculations allows us to conclude that the Klein–Fock–Gordon equation, unlike the Schrödinger equation, cannot describe the energy of the particle s-state in the magnetic field. It is elucidated that a correction for the relativistic energy level caused by the constant magnetic field is noticeable for the magnetic field H > 100.