Geodesic
Relativistic partial Green's functions of scattering states characterized by orbital quantum number $l=1$
Problemy fiziki, matematiki i tehniki, no. 3 (2021), pp. 7-13

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Green's functions of the quasipotential approach of quantum field theory are found in the relativistic configurational representation and are expressed in terms of elementary functions in case of scattering states characterized by orbital quantum number $l=1$ ($p$-states). Asymptotic properties of the Green's functions are determined at large values of the relativistic coordinate. It is shown that all the Green's functions coincide in the nonrelativistic limit with the partial Green's function of the Schrodinger equation. The equations for the corresponding partial wave functions of the scattering states are solved exactly in case of spherically symmetric potentials «$\delta$-sphere» and their superpositions. Characteristic features of the behavior of partial scattering cross sections for such potentials are determined.
Keywords: Green's functions, quasipotential approach, relativistic configurational representation, scattering states, $p$-states, delta-function potential. 
@article{PFMT_2021_3_a0,
     author = {V. N. Kapshai and A. A. Grishechkina},
     title = {Relativistic partial {Green's} functions of scattering states characterized by orbital quantum number $l=1$},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {7--13},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2021_3_a0/}
}
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V. N. Kapshai; A. A. Grishechkina. Relativistic partial Green's functions of scattering states characterized by orbital quantum number $l=1$. Problemy fiziki, matematiki i tehniki, no. 3 (2021), pp. 7-13. http://geodesic.mathdoc.fr/item/PFMT_2021_3_a0/