The solvable quantum mechanical model for the relativistic two-body system composed of spin-1/2 and spin-0 particles is constructed. The model includes the oscillator-type interaction through a combination of Lorentz-vector and -tensor potentials. Th
e analytical expressions for the wave functions and the order of the energy levels are discussed.
A new technique for constructing the relativistic wave equation for the two-body system composed of the spin-1/2 and spin-0 particles is proposed. The method is based on the extension of the SL(2,C) group to the Sp(4,C) one. The obtained equation inc
ludes the interaction potentials, having both the Lorentz-vector and Lorentz-tensor structure, exactly describes the relativistic kinematics and possesses the correct one-particle limits. The comparison with results of other approaches to this problem is discussed.
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $hbar$-expansions and suitable quantizatio
n conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As examples, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator and the Debye potential are considered.
A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and one spin-0 particle with unequal masses is constructed.
