对angular momentum的量化的评论：II。基于angular momentum算子第三分量的特征函数必须是单值周期函数的要求的分析
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
摘要：
讨论了角动量算符第三分量本征函数的单值性和周期性要求。这个条件，强加于不可观测的，经常被用来推导角动量的本征值只能是整数。我们重新审视的论点，根据这一要求和替代条件所施加的泡利，并表明，他们不遵循第一原则，因此这些限制可以下降。因此，我们得到了与[1]相同的结论：存在正则的、可归一化的本征函数，其本征值为非整数，因此，从理论观点来看，非整数角动量是完全容许的。形成角动量谱的本征值的性质问题仍然没有解决。从第一原理可以导出的是，角动量L的固定值对应于角动量的第三分量m的本征值的离散谱，其由关系式|m| =L-k，k= 0，1，.，[L]其中，[L]是L的整数部分。作为我们的本征函数分析的数学副产品，我们提出了一个替代的定义，允许保留初始平移不变性的基础上的一个复数的权力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
