### Abstract

Original language | American English |
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Pages (from-to) | 153-160 |

Number of pages | 136 |

Journal | Annals of Physics |

DOIs | |

State | Published - 1 Jan 2014 |

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### Cite this

*Annals of Physics*, 153-160. https://doi.org/10.1016/j.aop.2014.05.018

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*Annals of Physics*, pp. 153-160. https://doi.org/10.1016/j.aop.2014.05.018

**Quantum information entropies for position-dependent mass Schrödinger problem.** / Yañez-Navarro, G.; Sun, Guo Hua; Dytrych, T.; Launey, K. D.; Dong, Shi Hai; Draayer, J. P.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Quantum information entropies for position-dependent mass Schrödinger problem

AU - Yañez-Navarro, G.

AU - Sun, Guo Hua

AU - Dytrych, T.

AU - Launey, K. D.

AU - Dong, Shi Hai

AU - Draayer, J. P.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.aop.2014.05.018

DO - 10.1016/j.aop.2014.05.018

M3 - Article

SP - 153

EP - 160

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -