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

Wave functions of a particle with polarizability in the Coulomb potential