Quantum information entropies of the eigenstates for a symmetrically trigonometric Rosen–Morse potential

Abstract

Shannon entropy for the position and momentum eigenstates of the symmetrically trigonometric Rosen–Morse potential for the lower states n = 1–4 is evaluated. The position information entropies Sx for n = 1,2 are presented analytically. Some interesting features of the information entropy densities ρs(x) and ρs(p) are demonstrated graphically. We find that the ρs(p) is inversely proportional to the range of potential a and the Sx decreases with increasing the potential depth D. In particular, we note that the Sx might become negative for some given parameters a and D. The Bialynicki-Birula–Mycielski inequality is also tested for a number of states and is found to generally hold well.