Recent content by pprie003

I don't know why I did all that extra stuff. Still, won't this leave the ## \frac{1}{r^2}## in the angular terms? Should I factor out that term, then substitute the square of angular momentum operator?

Yes I did this problem, which separated nicely into 3 1-D Harmonic Oscillators, and was able to find the energy and first excited state wave fn as well as its degeneracy.

Sorry I left out info, I was having a hard time writing the code, but here is the rest of the work (the problem tells me to work in spherical coordinates): ## \frac {- \hbar ^2} {2m} \, \Big[\frac {1} {r^2} \, \frac{∂}{∂r} \ \Big(r^2 \frac {∂}{∂r} \Big) \, + \frac {1} {r^2 \sinθ} \frac{∂}{∂θ}...

Here is what I got: ## \frac {- \hbar ^2} {2m} \, \Big[\frac {1} {r^2} \, \frac{∂}{∂r} \ \Big(r^2 \frac {∂}{∂r} \Big) \, + \frac {1} {r^2 \sinθ} \frac{∂}{∂θ} \, \Big( \sinθ \frac {∂} {∂θ} \Big) + \frac {1}{r^2 \sin^2θ} \, \frac {∂^2}{∂φ^2} \Big]ψ + \frac {1}{2} m \,ω^2 \, r^2ψ \ = Eψ## Let...

Homework Statement What is the normalized ground state energy for the 3-D Harmonic Oscillator Homework Equations V(r) = 1/2m(w^2)(r^2) The Attempt at a Solution I started with the wave fn in spherical coordinates, and have tried using sep of variables, but keep getting stuck when trying to...