在分数的施罗丁格方程中,对于一个超模双井潜力的量子信息
R Santana-Carrillo1, J M Velázquez Peto2, Guo-Hua Sun1
1Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, Mexico City 07700, Mexico.
Entropy (Basel, Switzerland)
|July 29, 2023
概括
这项研究探讨了Shannon在分数施罗丁格方程中的,用于超标双井潜力. 减小的分数导数定位位置,而移位动量,它们的总和增加.
科学领域:
- 量子力学就是量子力学.
- 数学物理 数学物理
背景情况:
- 分数施罗丁格方程 (FSE) 使用分数计算扩展了量子力学.
- 超标双井潜力 (HDWP) 呈现出复杂的量子行为.
- 香农度量化了量子系统中的不确定性.
研究的目的:
- 在FSE中用HDPW调查位置和动量香农 (Sx, Sp).
- 分析分数导数顺序 (k) 对性质的影响.
- 检查,潜在深度 (u) 和BBM不等式之间的关系.
主要方法:
- 对于各种分数顺序 (k) 和潜在深度 (u) 的FSE数值解决.
- 计算位置和动量 香农密度 (ρs(x), ρs(p)).
- 分析局部化和脱局部化趋势.
主要成果:
- 递减分数导数 (k) 定位位置密度 (ρs(x)) 并移位动量密度 (ρs(p)).
- 位置 (Sx) 降低,而动量 (Sp) 随着k的减少而增加.
- 随着k的减少,输入量 (Sx + Sp) 的总和会增加.
- 贝克纳-比亚利尼尼基-比鲁拉-迈塞尔斯基 (BBM) 不等式尽管存在Sx,Sp和潜在深度 (u) 的变化,但仍然存在.
- 费舍尔随着HDPP深度 (u) 和分数导数 (k) 的下降而增加.
结论:
- 分数顺序显著影响量子系统的不确定性和定位.
- 分数量子力学的HDPP系统表现出独特的态行为.
- BBM不平等在这些系统中对量子信息提供了基本的约束.
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