Relativistic solutions for the spin-1 particles in the two-dimensional Smorodinsky-Winternitz potential

In this study, we investigate relativistic spin-1 particles in the V(x,y)=(ω02/2)(x2+y2)+k1/x2+k2/y2 type of Smorodinsky-Winternitz potentials. In the first case, since this Smorodinsky-Winternitz potential has two dimensions, the system was transformed into polar coordinates from Cartesian coordinates. By using Duffin-Kemmer-Petiau formalism with the non-central Smorodinsky-Winternitz potential in two dimensions, the exact bound state energy eigenvalues and corresponding eigenfunctions were determined within the framework of the asymptotic iteration method. Bound state eigenfunctions were obtained in terms of confluent hypergeometric functions.