Galilean Covariance and the Schrödinger Equation

Abstract

Galilei transformations are formulated in a 5-dimensional form and on such basis the non-relativistic quantum mechanics is reconstructed. Our approach has the following advantages over others'. (1) The Schrodinger wavefunctions are taken to be vector (not projective) representations of the Galilei group, so that (2) the problem here is considerably simplified. (3) The formulation proceeds in a way quite parallel to that of relativistic quantum mechanics, and what is most important, (4) Galilei covariance is manifest throughout.