Semiclassical treatment of an attractive inverse-square potential in an elastic medium with a disclination

Abstract

We analyze the interaction of the induced electric dipole moment of a neutral particle with an electric field in elastic medium with a charged disclination from a semiclassical point of view. We show that the interaction of the induced electric dipole moment of a neutral particle with an electric field can yield an attractive inverse-square potential, where it is influenced by the topology of the disclination. Then, by using the Wentzel, Kramers and Brillouin approximation based on the Langer transformation, we show that the centrifugal term of the radial equation must be modified due to the influence of the topology of the disclination. Besides, we obtain the bound states solutions to the Schrödinger equation.