Abstract
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.
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