Spin 2 Particle in Coulomb Field, the Non-relativistic Approximation

Abstract

The main goal of the present paper is to derive the non-relativistic system of equations for a spin 2 particle in presence of the external Coulomb field, then to solve it and to find the relevant energy spectra. We started with the known radial system of 39 equations derived for the case of a free particle and modified to take into account the presence of the Coulomb field. After eliminating the 28 components related to vector and 3-rank tensor, we get the system of second order for 11 components referring to scalar and symmetric tensor. In accordance with the parity restriction, it is divided in two subsystems, of 3 and 8 equations. For performing the non-relativistic approximation, we apply the method of projective operators constructed on the base of the matrix Γ0 of the initial matrix equation. Depending on parity, we derive two non-relativistic sub-systems, of 2 and 3 linked differential equations. With the use of the linear similarity transformation they are reduced to five separate equations with Schr¨odiger type non-relativistic structure, and evident energy spectra. The case of minimal quantum number of the total angular momentum, j = 0, should be considered separately.