Great answer but I kinda got lost in your second paragraph.
What does ##N_b(\vec{p},\sigma)## represent? I understand that ##\vec{p}## is the momentum but what is ##\sigma## and ##N_b## in your case?
When you write that ##N_b(\vec{p},\sigma)## are eigenstates of the Hamiltonian do you mean...
If we were to quantize the Dirac field using commutation relations instead of anticommutation relations we would end up with the Hamiltonian, see Peskin and Schroeder
$$
H = \int\frac{d^3p}{(2\pi)^3}E_p
\sum_{s=1}^2
\Big(
a^{s\dagger}_\textbf{p}a^s_\textbf{p}...
1. Homework Statement
A simple model atom is composed of a point-like nucleus with charge ##+Q## and an electron charge distribution
$$
\rho(\vec{r})=-\dfrac{\left|Q\right|}{\pi a^2 r}exp(-2r/a)
$$
where ##a## is a constant. Show that the ionization energy (the energy to remove the electron to...