论文标题
来自非相关量子机械氢原子中不同过渡的相等辐射频率
Equal Radiation Frequencies from Different Transitions in the Non-Relativistic Quantum Mechanical Hydrogen Atom
论文作者
论文摘要
在氢原子的非相关量子机械模型中，是否有两个不同的跃迁给出相同的频率？也就是说，氢原子中不同的能级过渡是否可以具有相同的光子辐射频率？这个问题是在博士学位期间提出的。 1997年在科罗拉多大学博尔德大学进行口试，在物理研究生中众所周知。我们展示了这个问题的一般解决方案，其中所有等频过渡对都可以从二聚体方程的解决方案集获得。这个有趣的难题是一个简单而具体的例子，说明了数字理论如何与量子系统相关，这是一个奇怪的主题，在理论物理学中出现，但通常对一般受众来说是无法访问的。
Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency? That is, can different energy level transitions in a hydrogen atom have the same photon radiation frequency? This question, which was asked during a Ph.D. oral exam in 1997 at the University of Colorado Boulder, is well-known among physics graduate students. We show a general solution to this question, in which all equifrequency transition pairs can be obtained from the set of solutions of a Diophantine equation. This fun puzzle is a simple yet concrete example of how number theory can be relevant to quantum systems, a curious theme that emerges in theoretical physics but is usually inaccessible to the general audience.
