The Wigner–Eckart theorem is central to the application of symmetry principles throughout atomic, molecular, and nuclear physics. Nevertheless, the theorem has a puzzling feature: it is dispensable for solving problems within these domains, since elementary methods suffice. To account for the significance of the theorem, I first contrast it with an elementary approach to calculating matrix elements. Next, I consider three broad strategies for interpreting the theorem: conventionalism, fundamentalism, and conceptualism. I argue that the conventionalist framework is unnecessarily pragmatic, while the fundamentalist framework requires more ontological commitments than necessary. Conceptualism avoids both defects, accounting for the theorem’s significance in terms of how it epistemically restructures the calculation of matrix elements. Specifically, the Wigner–Eckart theorem modularizes and unifies matrix element problems, thereby changing what we need to know to solve them.

Wigner-Eckart 定理是对称原理在原子、分子和核物理中应用的核心。然而，该定理有一个令人费解的特点：它对于解决这些领域内的问题是可有可无的，因为基本方法就足够了。为了说明该定理的重要性，我首先将其与计算矩阵元素的基本方法进行对比。接下来，我考虑解释该定理的三种广泛策略：约定主义、原教旨主义和概念主义。我认为约定主义框架是不必要的实用主义，而原教旨主义框架需要更多的本体论承诺而不是必要的。概念主义避免了这两个缺陷，说明了该定理在认知上重构矩阵元素计算的重要性。具体来说，