时间算子的广义Weyl关系及其与生存概率的关系
A generalized Weyl relation approach to the time operator and its connection to the survival probability
摘要：
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.在自伴T的情况下，这个关系等价于Weyl关系，并且对于一维自由粒子系统，它由Aharonov-Bohm时间算符T_0和自由哈密顿量H_0所满足。为了了解T_0的定性性质，我们考察了满足这种代数关系的算子T和H。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。
英文摘要：
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 T_0 and the free Hamiltonian H_0 for the one-dimensional free-particle system. In order to see the qualitative properties of T_0, 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.
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