• 文献检索
  • 文档翻译
  • 深度研究
  • 学术资讯
  • Suppr Zotero 插件Zotero 插件
  • 邀请有礼
  • 套餐&价格
  • 历史记录
应用&插件
Suppr Zotero 插件Zotero 插件浏览器插件Mac 客户端Windows 客户端微信小程序
定价
高级版会员购买积分包购买API积分包
服务
文献检索文档翻译深度研究API 文档MCP 服务
关于我们
关于 Suppr公司介绍联系我们用户协议隐私条款
关注我们

Suppr 超能文献

核心技术专利：CN118964589B侵权必究
粤ICP备2023148730 号-1Suppr @ 2026

文献检索

告别复杂PubMed语法，用中文像聊天一样搜索，搜遍4000万医学文献。AI智能推荐，让科研检索更轻松。

立即免费搜索

文件翻译

保留排版，准确专业，支持PDF/Word/PPT等文件格式，支持 12+语言互译。

免费翻译文档

深度研究

AI帮你快速写综述，25分钟生成高质量综述，智能提取关键信息，辅助科研写作。

立即免费体验

分数阶薛定谔方程中双曲势的量子信息熵

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation.

作者信息

Santana-Carrillo R, González-Flores Jesus S, Magaña-Espinal Emilio, Quezada Luis F, Sun Guo-Hua, Dong Shi-Hai

机构信息

Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, Ciudad de Mexico 07738, Mexico.

Research Center for Quantum Physics, Huzhou University, Huzhou 313000, China.

出版信息

Entropy (Basel). 2022 Oct 24;24(11):1516. doi: 10.3390/e24111516.

DOI:10.3390/e24111516
PMID:36359609
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9689018/
Abstract

In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schrödinger equation (the fractional derivative number (0<n≤2) by calculating position and momentum entropy. We find that the wave function will move towards the origin as the fractional derivative number n decreases and the position entropy density becomes more severely localized in more fractional system, i.e., for smaller values of n, but the momentum probability density becomes more delocalized. And then we study the Beckner Bialynicki-Birula−Mycieslki (BBM) inequality and notice that the Shannon entropies still satisfy this inequality for different depth u even though this inequality decreases (or increases) gradually as the depth u of the hyperbolic potential U1 (or U2) increases. Finally, we also carry out the Fisher entropy and observe that the Fisher entropy increases as the depth u of the potential wells increases, while the fractional derivative number n decreases.

摘要

在这项工作中，我们通过计算位置熵和动量熵，研究了分数阶薛定谔方程中两个双曲单阱势的香农信息熵（分数阶导数阶数(0 < n \leq 2)）。我们发现，随着分数阶导数阶数(n)减小，波函数将向原点移动，并且在更多分数阶系统中，位置熵密度变得更加严重地局域化，即对于较小的(n)值，但动量概率密度变得更加离域。然后我们研究了贝克纳 - 比亚林斯基 - 比鲁拉 - 米切尔斯基（BBM）不等式，并注意到即使随着双曲势(U1)（或(U2)）的深度(u)增加，该不等式逐渐减小（或增加），香农熵对于不同的深度(u)仍然满足该不等式。最后，我们还进行了费希尔熵的计算，并观察到随着势阱深度(u)增加，费希尔熵增加，而分数阶导数阶数(n)减小。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/28325108f8b6/entropy-24-01516-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/b18e35d414e9/entropy-24-01516-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/5cc77c317d59/entropy-24-01516-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/d70b00f9be96/entropy-24-01516-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/e69beeef2480/entropy-24-01516-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/b47b5fe4327b/entropy-24-01516-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/c6a490d58c7a/entropy-24-01516-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/1e3f413557fe/entropy-24-01516-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/873e68038569/entropy-24-01516-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/0b4061ad9a73/entropy-24-01516-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/5672d68ca3d4/entropy-24-01516-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/28325108f8b6/entropy-24-01516-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/b18e35d414e9/entropy-24-01516-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/5cc77c317d59/entropy-24-01516-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/d70b00f9be96/entropy-24-01516-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/e69beeef2480/entropy-24-01516-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/b47b5fe4327b/entropy-24-01516-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/c6a490d58c7a/entropy-24-01516-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/1e3f413557fe/entropy-24-01516-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/873e68038569/entropy-24-01516-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/0b4061ad9a73/entropy-24-01516-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/5672d68ca3d4/entropy-24-01516-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/055f/9689018/28325108f8b6/entropy-24-01516-g011.jpg

相似文献

1
Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation.分数阶薛定谔方程中双曲势的量子信息熵
Entropy (Basel). 2022 Oct 24;24(11):1516. doi: 10.3390/e24111516.
2
Quantum Information Entropy for a Hyperbolic Double Well Potential in the Fractional Schrödinger Equation.分数阶薛定谔方程中双曲双阱势的量子信息熵
Entropy (Basel). 2023 Jun 28;25(7):988. doi: 10.3390/e25070988.
3
Quantum Information Entropy for Another Class of New Proposed Hyperbolic Potentials.另一类新提出的双曲势的量子信息熵
Entropy (Basel). 2023 Sep 5;25(9):1296. doi: 10.3390/e25091296.
4
Quantum Information Entropies on Hyperbolic Single Potential Wells.双曲单势阱上的量子信息熵
Entropy (Basel). 2022 Apr 26;24(5):604. doi: 10.3390/e24050604.
5
Theoretic measure and thermal properties of a standard Morse potential model.标准莫尔斯势模型的理论测量与热性质
J Mol Model. 2023 Jan 10;29(2):34. doi: 10.1007/s00894-022-05441-z.
6
Fisher and Shannon Functionals for Hyperbolic Diffusion.双曲扩散的Fisher和Shannon泛函
Entropy (Basel). 2023 Dec 6;25(12):1627. doi: 10.3390/e25121627.
7
Characteristic features of Shannon information entropy of confined atoms.
J Chem Phys. 2005 Aug 15;123(7):074110. doi: 10.1063/1.2008212.
8
Numerical simulation of the space dependent fractional Schrödinger equation for London dispersion potential type.伦敦色散势类型的空间相关分数薛定谔方程的数值模拟。
Heliyon. 2020 Jul 18;6(7):e04495. doi: 10.1016/j.heliyon.2020.e04495. eCollection 2020 Jul.
9
Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials.球对称性和自旋对具有中心势的多维量子系统不确定性度量的影响。
Entropy (Basel). 2021 May 14;23(5):607. doi: 10.3390/e23050607.
10
Thermomagnetic properties and its effects on Fisher entropy with Schioberg plus Manning-Rosen potential (SPMRP) using Nikiforov-Uvarov functional analysis (NUFA) and supersymmetric quantum mechanics (SUSYQM) methods.采用 Nikiforov-Uvarov 函数分析 (NUFA) 和超对称量子力学 (SUSYQM) 方法研究 Schioberg 加 Manning-Rosen 势 (SPMRP) 下的热磁性质及其对 Fisher 熵的影响。
Sci Rep. 2023 May 20;13(1):8193. doi: 10.1038/s41598-023-34521-0.

引用本文的文献

1
Eigensolutions of generalized fractional Schrödinger equation with Hulthén-Hellmann potential and topological defects.具有胡尔特恩 - 赫尔曼势和拓扑缺陷的广义分数薛定谔方程的本征解
Sci Rep. 2025 Jul 2;15(1):23481. doi: 10.1038/s41598-025-07761-5.
2
Quantum Information Entropy for Another Class of New Proposed Hyperbolic Potentials.另一类新提出的双曲势的量子信息熵
Entropy (Basel). 2023 Sep 5;25(9):1296. doi: 10.3390/e25091296.
3
Quantum Information Entropy for a Hyperbolic Double Well Potential in the Fractional Schrödinger Equation.

本文引用的文献

1
Quantum Information Entropies on Hyperbolic Single Potential Wells.双曲单势阱上的量子信息熵
Entropy (Basel). 2022 Apr 26;24(5):604. doi: 10.3390/e24050604.
2
Analytical determination of theoretic quantities for multiple potential.多势的理论量的分析测定
Sci Rep. 2020 Oct 16;10(1):17542. doi: 10.1038/s41598-020-73372-x.
3
Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity.带 Kerr 型非线性的空间分数阶薛定谔方程中的光孤子、自聚焦和波崩溃。
分数阶薛定谔方程中双曲双阱势的量子信息熵
Entropy (Basel). 2023 Jun 28;25(7):988. doi: 10.3390/e25070988.
4
PCNN Model Guided by Saliency Mechanism for Image Fusion in Transform Domain.显著度机制引导的 PCNN 模型在变换域中的图像融合。
Sensors (Basel). 2023 Feb 23;23(5):2488. doi: 10.3390/s23052488.
Phys Rev E. 2018 Aug;98(2-1):022211. doi: 10.1103/PhysRevE.98.022211.
4
Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation.光束在分数阶薛定谔方程中的传播动力学
Phys Rev Lett. 2015 Oct 30;115(18):180403. doi: 10.1103/PhysRevLett.115.180403. Epub 2015 Oct 27.
5
Inequalities in fourier analysis on R.实数域上傅里叶分析中的不等式
Proc Natl Acad Sci U S A. 1975 Feb;72(2):638-41. doi: 10.1073/pnas.72.2.638.
6
Fractional quantum mechanics.分数量子力学。
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Sep;62(3 Pt A):3135-45. doi: 10.1103/physreve.62.3135.
7
New localization in a quasiperiodic system.
Phys Rev Lett. 1989 Jun 5;62(23):2714-2717. doi: 10.1103/PhysRevLett.62.2714.
8
Mobility edge in a model one-dimensional potential.
Phys Rev Lett. 1988 Oct 31;61(18):2144-2147. doi: 10.1103/PhysRevLett.61.2144.
9
Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom.
Phys Rev A. 1994 Oct;50(4):3065-3079. doi: 10.1103/physreva.50.3065.