Wow it is so much easier to manipulate the \upsilon(\rho) equation into the associated Laguerre ODE than to use the recursion relation. Thanks for your help!
The recursion relation i have is:
cj+1= \frac{j+L+1-n}{(j+1)(j+2L+2)}cj
for principle quantum number n, and orbital quantum number L, where the coefficients terminate after
jmax = n - L - 1
The definition I'm trying to match is the one in Arfken & Weber:
L^{k}_{N} =...
I'm in the first of 3 courses in quantum mechanics, and we just started chapter 4 of Griffiths. He goes into great detail in most of the solution of the radial equation, except for one part: translating the recursion relation into a form that matches the definition of the Laguerre polynomials...
Homework Statement
This is for my intro to General Relativity class, using Hartle's text Gravity: An intro to Einstein's GR.
12.1 "How many protons must combine to make one He nuclei every second to provide the luminosity of the Sun? Estimate how long the Sun could go on at this rate before...