当前位置: X-MOL 学术J. Math. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Heisenberg’s uncertainty principle associated with the Caputo fractional derivative
Journal of Mathematical Physics ( IF 1.2 ) Pub Date : 2021-04-13 , DOI: 10.1063/5.0038691
Pan Lian 1
Affiliation  

In this paper, we establish the Heisenberg’s uncertainty inequality associated with the Caputo derivative of order q ∈ (1, ) in the generalized Bargmann–Fock space. We also determine exactly when the equality occurs in the uncertainty inequality. It is done by estimating the growth of the eigenvalues of the commutator [Dq,zq]. We prove that the sequence of eigenvalues of [Dq,zq] tends to when the fractional order q belongs to (1, ). However, the sequence converges to zero when q belongs to (0, 1), which shows different behavior. Hence, only a weak uncertainty inequality is obtained for the latter case.

中文翻译:

海森堡的不确定性原理与Caputo分数导数相关

在本文中,我们建立与命令的卡普托衍生物相关联的海森堡的不确定性不等式q ∈(1,在广义巴格曼-福克空间)。我们还确定不确定性不平等中何时出现平等。通过估算换向器特征值的增长来完成[dqžq]。我们证明了特征值的序列[dqžq]趋于时分数阶q属于(1,)。但是,当q属于(0,1)时,序列收敛为零,这表明行为不同。因此,对于后一种情况,仅获得了弱的不确定性不等式。
更新日期:2021-04-30
down
wechat
bug