5 research outputs found
A new approach to perturbation theory for a Dirac particle in a central field
The explicit semiclassical treatment of logarithmic perturbation theory for
the bound-state problem within the framework of the Dirac equation is
developed. Avoiding disadvantages of the standard approach in the description
of exited states, new handy recursion formulae with the same simple form both
for ground and exited states have been obtained. As an example, the
perturbation expansions for the energy eigenvalues for the Yukawa potential
containing the vector part as well as the scalar component are considered.Comment: 12 pages, LaTe
Relativistic two-body equation based on the extension of the SL(2,C) group
A new approach to the two-body problem based on the extension of the
group to the one is developed. The wave equation with
various forms of including the interaction for the system of the spin-1/2 and
spin-0 particles is constructed. For this system, it was found that the wave
equation with a linear confinement potential involved in the non-minimal manner
has an oscillator-like form and possesses the exact solution.Comment: 9 pages, no figure
Oscillator model for the relativistic fermion-boson system
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. The analytical expressions for the wave functions and the
order of the energy levels are discussed.Comment: published version, 8 pages, 2 figure