The naïve Bohr quantization condition $\mathit{mvr}=n\hslash$ is applied to arbitrary spherically symmetric power-law potentials. The dependence of the energy eigenvalues on the principal quantum number n agrees with fully quantum mechanical results either exactly (for the hydrogen atom, the harmonic oscillator, and the infinite square well) or asymptotically (the linear potential). This naïve treatment can be used in precalculus, high-school, or “quantum theory for poets” expositions.

中文翻译：

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幂律势的朴素Bohr型量化

朴素的玻尔量化条件 $\mathit{录象机}=ñ\hslash$应用于任意球对称的幂律势。能量特征值对主量子数n的依赖性与完全量子力学结果完全一致（对于氢原子，谐波振荡器和无限方阱）或渐近（线性势）一致。这种幼稚的处理方式可用于微积分，高中或“诗人的量子理论”展览中。