Common fractions N₁/N₂, where N₁ and N₂ are small integers, are quite often used for a quantum-mechanical description of microcosm objects (for example, fractional charges of quarks and some quantum characteristics, such as particle spins). Recently the fractional quantum Hall effect has been discovered, and the common fractions considerably expand their presence in microcosm physics. The theory of the fractional quantum Hall effect has appeared nontrivial, so the Nobel Prize in physics was awarded in 1998 not only for the discovery of the effect itself by Daniel Tsui and Horst Störmer in 1982, but also for the theory developed by Robert Laughlin in 1983. And now one more sensational discovery has been made: common fractions have been detected during an analysis of experimental characteristics of hydrogen-like atoms and ions (with only one electron on the outer shell). It has appeared that the effective main quantum number of the outer shell electron subject to quantum defect (the Rydberg correction) can be expressed in common fractions N₁/N₂.

普通分数N ₁ / N ₂，其中N ₁和N ₂是小整数，经常用于微观宇宙物体的量子力学描述（例如，夸克的分数电荷和某些量子特性，例如粒子自旋）。最近，已经发现了分数量子霍尔效应，并且普通分数大大扩展了它们在微观物理学中的存在。分数量子霍尔效应的理论似乎是不平凡的，因此，1998年诺贝尔物理学奖不仅因丹尼尔·崔（Daniel Tsui）和霍斯特·斯托默（HorstStörmer）本身的发现而获得，也因罗伯特·劳克林（Robert Laughlin）于1989年提出1983年。现在又有了一个令人震惊的发现：在分析类氢原子和离子（外壳上只有一个电子）的实验特性时，已经检测到常见的馏分。₁ / N ₂。