An elementary, analytically soluble example of a pair of isospectral potentials is discussed. This example was developed in response to an inquiry by an undergraduate student who was intrigued by the widely used (but not often discussed in undergraduate courses) Rydberg–Klein–Rees (RKR) procedure for inverting rovibrational data to determine potential functions of diatomic molecules, which is based on the semiclassical (WKB) approximation. The pair of potentials discussed provide a clear elementary example of the insufficiency of the energy level spectrum to determine the potential, even in a case in which the bound states form a complete set.

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关于反转光谱数据以确定原子间势的本科生评论

讨论了一对等谱电位的一个基本的、解析可解的例子。这个例子是为了响应一名本科生的询问而开发的，他对广泛使用（但在本科课程中不经常讨论）的 Rydberg-Klein-Rees (RKR) 程序感兴趣，该程序用于反转振动数据以确定双原子分子的潜在功能，它基于半经典 (WKB) 近似。讨论的这对势提供了一个清晰的基本例子，说明了能级谱不足以确定势，即使在束缚态形成完整集的情况下也是如此。