A generalized Weyl relation approach to the time operator and its connection to the survival probability
A generalized Weyl relation approach to the time operator and its connection to the survival probability
复制标题
时间算子的广义 Weyl 关系方法及其与生存概率的联系
DOI：
10.1063/1.1346598
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发表时间：
2000
影响因子：
1.3
通讯作者：
M. Miyamoto
中科院分区：
文献类型：
--
作者：
M. Miyamoto
本文研究了与Hamilton算子满足正则对易关系的时间算子，利用算子对T和H之间的某种代数关系，其中T是对称的，H是自伴的.这个关系等价于Weyl关系，在自伴T的情况下，并且由Aharonov-Bohm时间算子T0和一维自由粒子系统的自由哈密顿量H 0满足。为了看到T0的定性性质，满足这个代数关系的算子T和H被检查。特别地，它表明，T的标准差是直接连接到生存概率，和H是绝对连续的。因此，可以得出结论，存在的运营商T意味着存在的散射态。它也表明，最小的不确定性状态不存在。这些运营商T和H，比一维自由粒子系统的其他例子，证明。
The time operator, an operator which satisfies the canonical commutation relation with the Hamiltonian, is investigated, on the basis of a certain algebraic relation for a pair of operators T and H, where T is symmetric and H self-adjoint. This relation is equivalent to the Weyl relation, in the case of self-adjoint T, and is satisfied by the Aharonov–Bohm time operator T0 and the free Hamiltonian H0 for the one-dimensional free-particle system. In order to see the qualitative properties of T0, the operators T and H satisfying this algebraic relation are examined. In particular, it is shown that the standard deviation of T is directly connected to the survival probability, and H is absolutely continuous. Hence, it is concluded that the existence of the operator T implies the existence of scattering states. It is also shown that the minimum uncertainty states do not exist. Other examples of these operators T and H, than the one-dimensional free-particle system, are demonstrated.