Quantum information entropies for position-dependent mass Schrödinger problem
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.
Publication Source (Journal or Book title)
Annals of Physics
Yañez-Navarro, G., Sun, G., Dytrych, T., Launey, K., Dong, S., & Draayer, J. (2014). Quantum information entropies for position-dependent mass Schrödinger problem. Annals of Physics, 348, 153-160. https://doi.org/10.1016/j.aop.2014.05.018