Homework Help: Isotropic 3-D harmonic oscillator

1. Apr 22, 2007

bcoats

1. The problem statement, all variables and given/known data
Use Frobenius’ method to solve the problem of the isotropic three dimensional
harmonic oscillator in polar coordinates. It is sufficient to
find the energy levels and degeneracies, but it would be nice to plot the
spectrum like we did for hydrogen. Be sure to introduce the natural
length scale and energy scale and to incorporate the asymptotic forms
at r = 0 and r = infinity of the radial wave function into your power series
solution. You will find that the recursion relation skips a term, i. e.,
relates c_j+2 to c_j . Thus two coefficients c_0 and c_1 are left undetermined.
How do you handle this situation? (Note that you can check

2. Relevant equations
See attachments. (Had to put them as images, I guess.) But it only let me put 3. a_0=hbar^2/(me^2), rho=r/(a_0), epsilon=-(E/R) where R=(me^4)/(2hbar^2)

3. The attempt at a solution
Writing down the equations is about as far as I've gotten. I think that the V(r) potential is right for the spherical (the last attached image) but I'm not sure. This stuff is just really too abstract for me.

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