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Scattering of Particles. Rutherford-Bohr Atom

Problem 6.21

A particle of mass \(m\) moves along a circular orbit in a centrosymmetrical potential field \(U(r)=k r^{2} / 2\). Using the Bohr quantization condition, find the permissible orbital radii and energy levels of that particle

Reveal Answer
 6.21. rn=nℏ/mω,En=nℏω, where n=1,2,….,ω==k/m.\begin{aligned} \text { 6.21. } r_{n}=\sqrt{n \hbar / m \omega}, & E_{n}=n \hbar \omega, \text { where } n=1,2, \ldots ., \omega=\\ =& \sqrt{k / m} . \end{aligned}
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