Geodesic
Relativistic scattering $s$-states problem for superposition of two potentials «$\delta$-sphere» type
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 7-12

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Exact solutions of relativistic two-particle equations for scattering $s$-states are obtained in cases of the $\delta$-function potential and superposition of two $\delta$-function potentials. Scattering amplitudes and phase shifts are calculated on the basis of wave functions found. The analysis of values obtained was carried out. As a result, the unitarity condition and vanishing conditions of scattering amplitudes are proved. It is shown that the non-relativistic limit of relativistic expressions obtained yields results which coincide with corresponding expressions which were found in the process of solving the Schrödinger equation.
Keywords: relativistic two-particle equation, relativistic configurational representation, delta-function potential, scattering amplitude, phase shift, unitarity condition, Ramsauer–Townsend effect.
Mots-clés : $S$-matrix 
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     author = {V. N. Kapshai and Yu. A. Grishechkin},
     title = {Relativistic scattering $s$-states problem for superposition of two potentials {\guillemotleft}$\delta$-sphere{\guillemotright} type},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {7--12},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_2_a0/}
}
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V. N. Kapshai; Yu. A. Grishechkin. Relativistic scattering $s$-states problem for superposition of two potentials «$\delta$-sphere» type. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 7-12. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a0/