On the wave functions and energy spectrum for a spin 1 particle in external Coulomb field

Abstract

Quantum-mechanical system -- spin 1 particle in external Coulomb field is studied on the base of the matrix Duffin-Kemmer-Petiau formalism with the use of the tetrad technique. Separation of the variables is performed with the help of Wigner functions. With the help of parity operator, the radial 10-equation system is divided into two subsystem of 4 and 6 equations that correspond to parity P=(-1)^{j+1} and P= (-1)^{j} respectively. The system of 4 equation is reduced to a second order differential equation which coincides with that arising in the case of a scalar particle in Coulomb potential. It is shown that the 6-equation system reduces to two different second order differential equations for a "main" function. One main equation reduces to a confluent Heun equation and provides us with energy spectrum. Another main equation is a more complex one, and any solutions for it are not constructed.