(adsbygoogle = window.adsbygoogle || []).push({}); 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

your answers against the Cartesian solution of the same problem.)

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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# Homework Help: Isotropic 3-D harmonic oscillator

Can you offer guidance or do you also need help?

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