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Bohr radii and energy levels of the harmonic oscillator

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An electron of mass m is in a circular orbit in the potential U=0.5 k r^2. Using Bohr's quantization rule, find the allowed orbital radii and energy levels of this electron.

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U is the potential energy of a harmonic oscillator, i.e. the force is proportional to minus the distance. If you differentiate U w.r.t. r then you get minus the force in the radial direction. As you can see, it is given by:

F_r = -k r (1)

In this problem it is assumed that the electron is in such ...

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