Bialynicki-Birula Mycielski Research Articles

Quantum information entropies of the eigenstates for the Pöschl—Teller-like potential

Shannon entropy for lower position and momentum eigenstates of Pöschl—Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ(x) moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter |V2|. Concerning the momentum information entropy density ρ(p), we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing |V2|. The Bialynicki—Birula—Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with |V2|. However, the variation of momentum information entropy is contrary to that of the position information entropy.

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 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.

Information entropy of conditionally exactly solvable potentials

We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki–Birula–Mycielski inequality has also been tested for a number of states.