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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.

- I . V . Dobrovolska, R . S . Tutik
- 1999

Abstract. 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… (More)

The new potential model for pionic hydrogen, constructed with the employment of the twobody relativistic equation, is offered. The relativistic equation, based on the extension of the SL(2, C) group to the Sp(4, C) one, describes the effect of the proton spin and anomalous magnetic moment in accordance with the results of the quantum electrodynamics. Within… (More)

- I . V . DOBROVOLSKA, R . S . Tutik
- 2001

In the past few decades intensive investigations have been carried out on the one-dimensional anharmonic oscillator because of both its role in the modeling of quantum field theory and its usefulness in atomic, and molecular physics . The conventional way to study the energy eigenvalues and eigenfunctions of this bound-state problem is the practical… (More)

- D . A . Kulikov, R . S . Tutik
- 2006 International Conference on Mathematical…
- 2006

The spectrum of the Dirac oscillator perturbed by the Coulomb potential is considered. The Regge trajectories for its bound states are obtained with the method of h-expansion. It is shown that the split of the degenerate energy levels of the Dirac oscillator in the Coulomb field is approximately linear in the coupling constant

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