Shannon information entropies for position-dependent mass Schrödinger problem with a hyperbolic well

doi:10.1088/1674-1056/24/10/100303

Abstract The Shannon information entropy for the Schrödinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position S_x and momentum S_p information entropies for six low-lying states are calculated. We notice that the S_x decreases with the increasing mass barrier width a and becomes negative beyond a particular width a, while the S_p first increases with a and then decreases with it. The negative S_x exists for the probability densities that are highly localized. We find that the probability density ρ(x) for n=1, 3, 5 are greater than 1 at position x=0. Some interesting features of the information entropy densities ρ_s(x) and ρ_s(p) are demonstrated. The Bialynicki-Birula-Mycielski (BBM) inequality is also tested for these states and found to hold.

Keywords: position-dependent mass Shannon information entropy hyperbolic potential Fourier transform

Received: 15 April 2015
Revised: 21 May 2015
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	03.65.Ge	(Solutions of wave equations: bound states)
	03.67.-a	(Quantum information)

Corresponding Authors: Dong Shi-Hai
E-mail: dongsh2@yahoo.com

Cite this article:

Sun Guo-Hua, Dušan Popov, Oscar Camacho-Nieto, Dong Shi-Hai Shannon information entropies for position-dependent mass Schrödinger problem with a hyperbolic well 2015 Chin. Phys. B 24 100303

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Shannon information entropies for position-dependent mass Schrödinger problem with a hyperbolic well

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