Quantum information entropies for position-dependent mass Schrödinger problem

G. Yañez-Navarro, Instituto Politécnico Nacional
Guo Hua Sun, Universidad Autónoma del Estado de México
T. Dytrych, Louisiana State University
K. D. Launey, Louisiana State University
Shi Hai Dong, Instituto Politécnico Nacional
J. P. Draayer, Louisiana State University


The Shannon entropy for the position-dependent Schrödinger 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 ρs (x) and ρs (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. © 2014 Elsevier Inc.