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

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

中国物理B ›› 2015, Vol. 24 ›› Issue (10): 100303-100303.doi: 10.1088/1674-1056/24/10/100303

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

Sun Guo-Hua^a, Dušan Popov^b, Oscar Camacho-Nieto^c, Dong Shi-Hai^c

a Cátedra CONACyT, Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, Mexico D. F. 07738, Mexico;
b Politehnica University Timisoara, Department of Physical Foundations of Engineering, Bd. V. Parvan No. 2, 300223Timisoara, Romania;
c CIDETEC, Instituto Politécnico Nacional, UPALM, Mexico D. F. 07700, Mexico

收稿日期:2015-04-15 修回日期:2015-05-21 出版日期:2015-10-05 发布日期:2015-10-05

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

Sun Guo-Hua^a, Dušan Popov^b, Oscar Camacho-Nieto^c, Dong Shi-Hai^c

a Cátedra CONACyT, Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, Mexico D. F. 07738, Mexico;
b Politehnica University Timisoara, Department of Physical Foundations of Engineering, Bd. V. Parvan No. 2, 300223Timisoara, Romania;
c CIDETEC, Instituto Politécnico Nacional, UPALM, Mexico D. F. 07700, Mexico

Received:2015-04-15 Revised:2015-05-21 Online:2015-10-05 Published:2015-10-05
Contact: Dong Shi-Hai E-mail:dongsh2@yahoo.com

摘要/Abstract

摘要： 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.

关键词: position-dependent mass, Shannon information entropy, hyperbolic potential, Fourier transform

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.

Key words: position-dependent mass, Shannon information entropy, hyperbolic potential, Fourier transform

中图分类号: (Quantum mechanics)

03.65.-w

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

Sun Guo-Hua, Dušan Popov, Oscar Camacho-Nieto, Dong Shi-Hai. Shannon information entropies for position-dependent mass Schrödinger problem with a hyperbolic well[J]. 中国物理B, 2015, 24(10): 100303-100303.

Sun Guo-Hua, Dušan Popov, Oscar Camacho-Nieto, Dong Shi-Hai. Shannon information entropies for position-dependent mass Schrödinger problem with a hyperbolic well[J]. Chin. Phys. B, 2015, 24(10): 100303-100303.

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

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

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