# Homework Help: Quantizing the oscillator. I'm having trouble getting a real number for the velocity

1. Oct 5, 2011

### nymphidius

1. The problem statement, all variables and given/known data

Use Bohr's rule, L=n$\hbar$, to find the quantized speeds, radii, and energies for circular orbits of a particle of mass m bound to the origin by the Hooke's-law force, F(r) = -Kr.

2. Relevant equations

mass=m

ƩF=ma

F(r)=-kr

L=n$\hbar$

p=mvr

mvr=n$\hbar$

r=n$\hbar$/mv (a)

3. The attempt at a solution

mv²/r=-kr

mv²=-kr² (b)

subbing (a) into (b)

mv²=-kn²$\hbar²$/m²v²

solving for v...

(v²)²=-kn²$\hbar²$/m³

v=(-kn²$\hbar²$/m³)^¼

and this is where I get stuck because of the negative sign in the 4th root of v. If I make ma=kr it works out, BUT it seems cheap just to change the law from -kr to kr.

Last edited: Oct 5, 2011