PAULI EQUATION IN CURVILINEAR COORDINATES OF MINKOWSKI SPACE, SEPARATING THE VARIBLES

Abstract

The non-relativistic Pauli approximation for a spin ½ particle is studied in arbitatry curvilinear orthogonal coordinates.The final goal is to develop ф unified approach to separating the variables in equation for s spin ½ particle in all 12 system of orthogonal coordinates in the flat space, first in more simple Pauli approximation. A general structure for the covariant equation is derived Pauli equation in arbitrary orthogonal coordinates, it includes the relevant tetrads and Ricci rotation coefficients. Because the possibility to develop a unified approach to separating the variables in ordinary presentation of the covariant Pauli equation is rather problematitic, other way for studying the problem is proposed. It is based on transforming the usual 2-component Pauli equation to an equivalent system of first order four differential equations, by introducing two auxiliary components, because it is known that the task of separating the variables in the system of differential equations in partial derivatives may be solved easier for the first order systems. One simple example for illustating this approach, is given; a spin ½ particle problem in presence of external magnetic field when using the сylindrical coordinates.