Recent content by Turbotanten

  1. Turbotanten

    A What does it mean for the Hamiltonian to not be bounded?

    Thanks! Now I finally get it!
  2. Turbotanten

    A What does it mean for the Hamiltonian to not be bounded?

    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...
  3. Turbotanten

    A What does it mean for the Hamiltonian to not be bounded?

    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}...
  4. Turbotanten

    Find the ionization energy of a simple model atom

    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...
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