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## Homework Statement

The general quantization of motion in circular orbits is obtained by combining the equation of motion ## \frac{mv^2}{r} = |\frac{dU(r)}{dr}| ## with the angular momentum quantization condition ## mvr=n\hbar ## Use this procedure to calculate the spectrum for circular motion in the potential ## U = (F_0)r ##

## Homework Equations

I think you need to use one of the series to find the spectrum but I'm quite lost on how to get there.

## The Attempt at a Solution

I assume you make a substitution from ## mvr=n\hbar ## to quantize the equation of motion. I don't know if you use the given potential at first, and use its derivative ## |F_0| ##?

The form of the answer highly suggests using a series, however there are terms in it that I don't have in the initial conditions so I don't think I know where to go from here.