# General Quantization of Motion in Circular Orbits

1. Feb 13, 2014

### wawitz

For this question, I have to obtain a general quantization of motion in circular orbits by combining the equations (Where U(r) is potential energy):
(mv2)/r= |(dU(r))/dr|

With the angular momentum quantization of: mvr= nℏ

Then use this to calculate the spectrum for circular motion in a potential of U = F0r.

After combining these equations, along with E = Ke + Pe (for kinetic and potential energies), I obtained this equation:
En= 3/2*(n4/34/3 F02/3+F02/3 n2/32/3)/m1/3

The next step confuses me. To obtain a spectrum, I would have to use the relation ∆E=hc/λ; however this requires a difference of energies for ΔE. Would this mean setting up an equation for En+1 – En, using the equation I found for En?

2. Feb 14, 2014

### BvU

Hello Witz and welcome to PF. There is a pretty strict rule here that you make use of the template. In this case even I can see the usefulness: you have to obtain a general quantization. That's what you have done, so you are finished.

Why contnue? What is triggering the spectrum adventure ?
(You have an idea, why not follow up on it?)