Wave functions of a particle with polarizability in the Coulomb potential

Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single second order differential equation, which among the Coulomb term includes an additional interaction term of the form \sigma \alpha^{2} / M^{2}r^{4}. Various physical regimes exist that is demonstrated by examining the behavior of the curves of generalized squared radial momentum P^{2}(r). Eigenstates of the equations can be constructed in terms of double confluent Heun functions. Numerical analysis proves the existence of the bound states in the system; the lowest energy level and corresponding solution are calculated based on generalization of Ritz variational procedure.