Geodesic
Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$ in the relativistic configurational representation
Problemy fiziki, matematiki i tehniki, no. 3 (2023), pp. 12-15

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The approximate analytical solutions of the one-dimensional Logunov-Tavkhelidze equation in integral form, that describes bound states, with a model potential of the form$(\rho^2+\rho_0^2)^{-1}$ in the relativistic configuration representation are found. To solve the problem an approximate transformation of the relativistic integral equation in the momentum representation to the Sturm–Liouville problem for the Schrödinger equation with a potential in the form of the modified Pöschl–Teller potential well is performed.
Mots-clés : Logunov–Tavkhelidze equation, Sturm–Liouville problem
Keywords: model potential, relativistic configurational representation, momentum representation, approximate analytical solution, Schrödinger equation, modified Pöschl–Teller potential, hypergeometric series, energy quantization condition. 
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     author = {Yu. A. Grishechkin and A. V. Buzhan and V. N. Kapshai},
     title = {Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$  in the relativistic configurational representation},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {12--15},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2023_3_a1/}
}
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Yu. A. Grishechkin; A. V. Buzhan; V. N. Kapshai. Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$  in the relativistic configurational representation. Problemy fiziki, matematiki i tehniki, no. 3 (2023), pp. 12-15. http://geodesic.mathdoc.fr/item/PFMT_2023_3_a1/