Quantum Defect and Common Fractions

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.