Revisiting Bohr's quantization hypothesis for the atomic orbitals

Is the Bohr's quantization hypothesis necessary ?

We deduce the quantization of Bohr's hydrogen's atomic orbit without using his hypothesis of angular momentum quantization. We show that his hypothesis is nothing more than a consequence of the Planck's energy quantization.

Bohr's atomic model revisited

Bohr's atomic model, its relationship to the radiation spectrum of the hydrogen atom and the inherent hypotheses are revisited. It is argued that Bohr could have adopted a different approach, focusing his analyzes on the stationary orbit of the electron and its decomposition on two harmonic oscillators and then imposing, as actually he did, Planck's quantization for the oscillators' energies. Some consequences of this procedure are examined.

径向幂次类势：从 Bohr-Sommerfeld $S$ 态能量到精确能量

Radial power-like potentials: from the Bohr-Sommerfeld $S$-state energies to the exact ones

本研究将 Bohr-Sommerfeld 量子化条件推广至 $d$ 维幂次类径向势，引入 WKB 修正得到精确量子化条件，可重现 $S$ 态精确能量，并验证了多种势与维度下的有效性。