标题： 使用量子哈密顿-雅可比形式的 Hartmann 和环形势能的能谱 显示英文标题

标题： Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton-Jacobi formalism

摘要： 在本工作中，我们将精确量子化条件应用于角动量和径向量子作用变量，该条件是在Padgett和Leacock的量子哈密顿-雅可比形式框架内提出的，适用于可分离且非中心的Hartmann和环形振子势。这两个系统的能量光谱被准确地得到了。 显示英文摘要

摘要： In the present work, we apply the exact quantization condition, introduced within the framework of Padgett and Leacock's quantum Hamilton-Jacobi formalism, to angular and radial quantum action variables in the context of the Hartmann and the ring-shaped oscillator potentials which are separable and non central. The energy spectra of the two systems are exactly obtained.