- #1
emilionovati
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- TL;DR Summary
- Problema in the interpretation of the Feynman solution of the Schrodinger equation for the hydrogen atom
Reading the classical Feynman lectures, I encounter the formula(19.53) that gives the radial component of the wave function:
$$
F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k
$$
that, for ##n=l+1## becomes
$$
F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n
$$
To find ##a_n## I use the recursive formula (19.50), but here I have problem. Using $k+1=n=l+1$ I find a division by zero.
$$
a_n =\frac{2\left( \frac{n-1}{n}-1 \right)}{(n-1)n-(n-1)n}
$$
so clearly I have a mistake. But where is it?
$$
F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k
$$
that, for ##n=l+1## becomes
$$
F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n
$$
To find ##a_n## I use the recursive formula (19.50), but here I have problem. Using $k+1=n=l+1$ I find a division by zero.
$$
a_n =\frac{2\left( \frac{n-1}{n}-1 \right)}{(n-1)n-(n-1)n}
$$
so clearly I have a mistake. But where is it?