Wave functions of a particle with polarizability in the Coulomb potential

V. Kisel, G. Krylov, E. Ovsiyuk, M. Amirfachrian, V. Red'kov

Published 2011-09-15Version 1

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.