ST¨UCKELBERG PARTICLE IN EXTERNAL MAGNETIC FIELD. THE METHOD OF PROJECTIVE OPERATORS
We study the St¨uckelberg equation for a relativistic particle with two spin states S = 1 and S = 0 in the presence of an external uniform magnetic field. The particle is described by an 11-component wave function consisting of a scalar, a vector, and an antisymmetric tensor. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, a system for 11 radial functions is obtained. Its solution is based on the use of the Fedorov-Gronsky method, in which all 11 radial functions are expressed in terms of three main functions. Exact solutions with cylindrical symmetry are constructed. Three series of energy levels are found.