论文标题
对角动量的量化：ii。基于对角动量操作员的第三个成分的特征功能必须是单个有价值的周期性函数的分析
Critical comments on the quantization of the angular momentum: II. Analysis based on the requirement that the eigenfunction of the third component of the operator of the angular momentum must be a single valued periodic function
论文作者
论文摘要
我们讨论了角动量操作员第三个组成部分的单个值和周期性的要求。这种条件施加在不可观察的情况下，通常用于得出角动量的特征值只能是整数。我们根据保利（Pauli）施加的替代条件重新审视论点，并表明它们不遵守第一原则，因此这些约束可能会下降。因此，我们得出与[1]中相同的结论：从理论上的角度来看，具有非整合特征值的规则，可正常的本征函数是完全可以接受的。形成角动量谱系的特征值本质的问题保持开放。可以从第一原则中得出的是，角动量L的固定值对应于角动量第三部分的特征值的离散频谱，m，由关系| m | = m | = l-k = 0,1，k = 0,1，...，...，...，[l]，其中[l]是l. as a as a as a a as a as a a a a as a a a a a a a a a a s a a a a a a a a a a a相对的一部分。复杂数字的功率允许保持基础的初始翻译不变性。
We discuss the requirement of single valuedness and periodicity of eigenfunction of the third component of the operator of angular momentum. This condition, imposed on a non observable, is often used to derive that the eigenvalues of angular momentum could be only integer. We reexamine the arguments based on this requirement and alternate condition imposed by Pauli and show that they do not follow from the first principles and therefore these constraints can dropped. Consequently, we arrive to the same conclusion as in [1]: there exist regular, normalizable eigenfunctions with the non-integer eigenvalues thus a non-integer angular momentum is perfectly admissible from the theoretical viewpoint. The issue of the nature of eigenvalues forming the spectrum of the angular momentum remains open. What can be derived from the first principles is that to a fixed value of the angular momentum L corresponds a discrete spectrum of eigenvalues of the third component of the angular momentum, m, defined by the relation |m|=L-k, k=0,1,...,[L], where [L] is an integer part of L. As a mathematical byproduct of our analysis of eigenfunctions, we present an alternate definition of a power of a complex number allowing to retain initial translational invariance of a base.
