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

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 S_x for n = 1,2 are presented analytically. Some interesting features of the information entropy densities ρ_s(x) and ρ_s(p) are demonstrated graphically. We find that the ρ_s(p) is inversely proportional to the range of potential a and the S_x decreases with increasing the potential depth D. In particular, we note that the S_x 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.