PHYSICS

Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$ in the relativistic configurational representation

Yu. A. Grishechkin, A. V. Buzhan, V. N. Kapshai

Francisk Skorina Gomel State University

Abstract: 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.

Keywords: Logunov–Tavkhelidze equation, model potential, relativistic configurational representation, momentum representation, Sturm–Liouville problem, approximate analytical solution, Schrödinger equation, modified Pöschl–Teller potential, hypergeometric series, energy quantization condition.

UDC: 539.12.01

Received: 14.08.2023

DOI: 10.54341/20778708_2023_3_56_12