Abstract
New fundamental (Galilean invariant) dynamical equations for four- component spinor wavefunctions are derived by using a different phase function than the Schrodinger phase function. The derived equations are called the generalized Levy-Leblond and generalized Schrodinger equa- tions because these equations reduce to the standard Levy-Leblond and Schrodinger equations when the Schrodinger phase function is used. The generalized and standard equations describe the same free elementary particles with spin 1/2, however, masses of the particles described by these equations are not the same as the generalized equations automati- cally account for particles with larger masses. This has important phys- ical implications as it shows that elementary particles with the same physical properties but different masses can result from using phase functions different than the Schrodinger phase function. Therefore, the main conclusion of this paper is that the existence of the three currently known families of elementary particles in the Standard Model of particle physics can be theoretically accounted for by choosing different phase functions.
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