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.