Quantum information entropies for position-dependent mass Schrödinger problem

G. Yañez-Navarro, Guo Hua Sun, T. Dytrych, K. D. Launey, Shi Hai Dong, J. P. Draayer

Research output: Contribution to journalArticlepeer-review

82 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)153-160
Number of pages8
JournalAnnals of Physics
Volume348
DOIs
StatePublished - Sep 2014

Keywords

  • Null potential
  • Position-dependent mass
  • Quantum information entropy

Fingerprint

Dive into the research topics of 'Quantum information entropies for position-dependent mass Schrödinger problem'. Together they form a unique fingerprint.

Cite this