PHYSICS

Numerical solution of the two-dimensional Logunov–Tavkhelidze equation for Gaussian potential in the relativistic configuration representation

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

Francisk Skorina Gomel State University

Abstract: Numerical solutions are obtained for the two-dimensional partial-wave integral quasipotential equations in the relativistic configuration space representation, describing the bound states of a system of two scalar particles of equal mass interacting via a Gaussian potential. A non-trivial spectral property is established: within certain ranges of the potential parameters, the ground state possesses a wave function with one, two or more nodes. The limiting transition is demonstrated as the Gaussian potential degenerates into the singular “delta-circle” potential: the numerical solutions asymptotically approach those for this limiting case.

Keywords: two-dimensional Logunov–Tavkhelidze equation, relativistic configurational representation, momentum representation, two-dimensional Green’s function, wave function, two-particle system, bound states, Gaussian potential, delta-circle potential.

UDC: 539.12.01

Received: 11.06.2025

DOI: 10.54341/20778708_2025_3_64_56