THE SOBOLEV INEQUALITY AND THE TSALLIS ENTROPIC UNCERTAINTY RELATION

The Heisenberg uncertainty relation is expressed in terms of the Tsallis entropies associated with the conjugate coordinate and momentum probability densities. By rewriting this in terms of a positive joint probability distribution suggested by Cohen and coworkers, a different insight into the statistical dependence of the quantum variables is obtained. A discussion of how this improves the previous results on this subject is given.