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Title: 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{sub x} and momentum S{sub 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{sub x} entropy as well as for the Fourier transformed wave functions, while the S{sub p} quantity is calculated numerically. We notice the behavior of the S{sub 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{sub p} on the width is contrary to the one for S{sub x}. Some interesting features of the information entropy densities ρ{sub s}(x) and ρ{sub 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.
Authors:
 [1] ;  [2] ;  [3] ;  [3] ;  [1] ;  [4] ;  [3]
  1. Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, UPALM, Mexico D. F. 07738 (Mexico)
  2. Centro Universitario Valle de Chalco, Universidad Autónoma del Estado de México, Valle de Chalco Solidaridad, Estado de México, 56615 (Mexico)
  3. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)
  4. (United States)
Publication Date:
OSTI Identifier:
22403384
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 348; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; ENTROPY; FOURIER TRANSFORMATION; MASS; PARTICLES; POTENTIALS; PROBABILITY DENSITY FUNCTIONS; QUANTUM INFORMATION; SCHROEDINGER EQUATION; WAVE FUNCTIONS