On the Separation of Variables for the Laplace Equation $\Delta \psi + K^2 \psi = 0$ in Two- and Three-Dimensional Minkowski Space

Abstract

Using well established methods we classify all coordinate systems in two-dimensional Minkowski space which allow a separation of variables of the Laplace equation $\Delta \psi + K^2 \psi = 0$. With each such coordinate system we associate an operator L which determines the choice of basis functions. The connection between these operators and symmetric second order operators in the generators of the group $E(1,1)$ is discussed. We also give a classification of all orthogonal separable coordinate systems in three-dimensional Minkowski space.