Exact solutions of the two-dimensional Logunov–Tavkhelidze equation with a superposition of «delta-circle» potentials in coordinate representation

In momentum representation for describing bound states of a system of two scalar particles with equal mass, exact and approximate solutions of the two-dimensional Logunov-Tavkhelidze equation were obtained for four variants of relativistic generalizations of separable potentials in momentum representation, which in coordinate representation appear as superpositions of «delta-ring» potentials. Exact and approximate energy quantization conditions were derived for both a single «delta-ring» potential and a superposition of two such potentials. It was established that for a fixed value of the azimuthal quantum number, the aforementioned particle systems may have one bound state, two bound states, or none at all, depending on the system parameters. The partial wave functions were obtained and analyzed in momentum representation, followed by transformation to coordinate representation. It was shown that the partial wave functions in momentum representation possess an infinite number of zeros, while in coordinate representation, the number of zeros equals the state number.

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