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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{PFMT_2023_3_a1,
     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/}
}
TY  - JOUR
AU  - Yu. A. Grishechkin
AU  - A. V. Buzhan
AU  - V. N. Kapshai
TI  - Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$  in the relativistic configurational representation
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2023
SP  - 12
EP  - 15
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2023_3_a1/
LA  - ru
ID  - PFMT_2023_3_a1
ER  - 
%0 Journal Article
%A Yu. A. Grishechkin
%A A. V. Buzhan
%A V. N. Kapshai
%T Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$  in the relativistic configurational representation
%J Problemy fiziki, matematiki i tehniki
%D 2023
%P 12-15
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2023_3_a1/
%G ru
%F PFMT_2023_3_a1
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/

[1] V.N. Kapshai, T.A. Alferova, “Relativistic two-particle onedimensional scattering problem for superposition of $\delta$-potentials”, J. Phys. A, 32 (1999), 5329–5342 | DOI | MR | Zbl

[2] V.N. Kapshai, T.A. Alferova, “One-dimensional relativistic problems on bound states and scattering for a superposition of two $\delta$-potentials”, Russian Physics Journal, 45 (2002), 1–9 | DOI

[3] V.N. Kapshai, S.I. Fialka, “Resheniya relyativistskikh dvukhchastichnykh uravnenii s proizvolnym orbitalnym momentom”, Izvestiya VUZov. Fizika, 60:1 (2017), 34–43 | Zbl

[4] V.N. Kapshai, N.B. Skachkov, “Tochnye resheniya kvazipotentsialnykh uravnenii dlya kulonovskogo i lineinogo zapirayuschego potentsialov”, TMF, 55:2 (1983), 236–245

[5] Z. Flyugge, Zadachi po kvantovoi mekhanike, v 2 t., v. 1, 3-e izd., LKI, M., 2010, 344 pp.

[6] L.D. Landau, E.M. Lifshits, Teoreticheskaya fizika, v 10 t., v. 3, Kvantovaya mekhanika: nerelyativistskaya teoriya, 5-e izd., Fizmatlit, M., 2002, 808 pp.

[7] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i tablitsami, Nauka, M., 1979, 830 pp.