The Q-Space Deformed Wave Equation

Abstract

Let q∈0,1. We know that, when q tends to 1, we recover “classical” quantum mechanics. However, when q is not equal to one, we have a theory of quantum mechanics in a spacetime, i.e., a theory where the vacuum has a nonzero energy density. As a q-analogue on the space variable of the wave equation, we introduce the q-space wave equation. Solutions of these equations are given for q∈0,1 and for q⟶0. Since some states have more spin degrees of freedom than the physical particle has, the q-space wave equations remove the additional degrees of freedom.