Semiclassical position and momentum information entropy for sech2 and a family of rational potentials

The classical and semiclassical position and momentum information entropies for the reflectionless sech2 potential and a family of rational potentials are obtained explicitly. The sum of these entropies is of interest for the entropic uncertainty principle that is stronger than the Heisenberg uncertainty relation. The analytic results relate the classical period of the motion, total energy, position and momentum entropy, and dependence upon the principal quantum number n. The logarithmic energy dependence of the entropies is presented. The potentials considered include as special cases the attractive delta function and square well. PACS Nos.: 03.67–a, 03.65.Sq, 03.65.Ge, 03.65.–w