论文标题
球形坐标中的普遍不确定性关系
Generalized uncertainty relations in spherical coordinates
论文作者
论文摘要
遵循Weil方法，我们将任意两个操作员的海森伯格 - 罗伯逊不确定性关系推广。考虑在球形坐标中进行考虑，其中远处变量受到一侧的限制。由于这个原因，必须考虑径向波函数和操作员的原点处的合适边界条件。因此，与传统方法相比，会出现额外的表面术语。这些额外的术语是针对各种可解决势能计算的，并研究了它们的影响。最后，还分析了时间能量不确定性关系。讨论了我们的方法与我们的方法之间的一些差异，其中考虑了直接差异的直接产品。
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason accounting of suitable boundary condition at the origin for radial wave functions and operators is necessary. Therefore, there arise extra surface terms in comparison with traditional approaches. These extra terms are calculated for various solvable potentials and their influence is investigated. At last, the time-energy uncertainty relations are also analysed. Some differences between our approach and that, in which a direct product for separate variances were considered are discussed.
