Homework Problems

1. Calculate the shifts in the hydrogen ground states due to a 1 kilogauss magnetic field.

2. Consider positronium, a hydrogen-like atom consisting of an electron and a positron (anti-electron). Calculate the fine structure of positronium for $n=1$ and $n=2$. Determine the hyperfine structure for the ground state. Compute the energy shifts in eV.

3. List the spectroscopic states allowed that arise from combining ($s={1\over 2}$ with $l=3$), ($s={2}$ with $l=1$), and ( $s_1={1\over 2},\quad s_2=1$ and $l=4$).