Quantum information entropies for position-dependent mass Schrodinger problem

The Shannon entropy for the position-dependent Schrodinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S-x and momentum S-p information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S-x entropy as well as for the Fourier transformed wave functions, while the S-p quantity is calculated numerically. We notice the behavior of the S-x, entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S-p on the width is contrary to the one for S-x. Some interesting features of the information entropy densities rho(s)(x) and rho(s)(P) are demonstrated. In addition, the Bialynicki-Birula-Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases. (C) 2014 Elsevier Inc. All rights reserved.