Exact solutions of the two-dimensional Logunov–Tavkhelidze equation for «delta-circle» potentials in the relativistic configuration representation

In this work, exact solutions are obtained for two-dimensional partial integral equations of the Logunov-Tavkhelidze type for a system of two particles of equal mass in the case of a «delta-circle» potential and a superposition of two such potentials, defined in the relativistic configuration representation. It is shown that for a single «delta-circle» potential, depending on its parameters, the system can have either one bound state or none at all. For a superposition of two «delta-circle» potentials, cases with one or two bound states, or their absence, are possible. Analysis of the wave functions revealed differences in their properties across different representations: in the relativistic configuration representation, the number of zeros of the partial wave function equals the state number of the particle system, whereas in the momentum representation, the number of zeros exceeds that in the configuration representation. The nonrelativistic limit of the obtained solutions is found, which agrees with the solutions of the two-dimensional Schrödinger equation for similar potentials in the momentum and coordinate representations.

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