Quantum information entropies for a squared tangent potential well

The particle in a symmetrical squared tangent potential well is studied by examining its Shannon information entropy and standard deviations. The position and momentum information entropy densities ^ρs(x), ^ρs(p) and probability densities ρ(x), ρ(p) are illustrated with different potential range L and potential depth U. We present analytical position information entropies ^Sx for the lowest two states. We observe that the sum of position and momentum entropies ^Sx and ^Sp expressed by Bialynicki-Birula-Mycielski (BBM) inequality is satisfied. Some eigenstates exhibit entropy squeezing in the position. The entropy squeezing in position will be compensated by an increase in momentum entropy. We also note that the ^Sx increases with the potential range L, while decreases with the potential depth U. The variation of ^Sp is contrary to that of ^Sx.