Homework Problems

1. Consider the fine structure of the $n=2$ states of the hydrogen atom. What is the spectrum in the absence of a magnetic field? How is the spectrum changed when the atom is placed in a magnetic field of 25,000 gauss? Give numerical values for the energy shifts in each of the above cases. Now, try to estimate the binding energy for the lowest energy $n=2$ state including the relativistic, spin-orbit, and magnetic field.

2. Verify the relations used for ${1\over r}$, ${1\over r^2}$, and ${1\over r^3}$ for hydrogen atom states up to $n=3$ and for any $n$ if $l=n-1$.

3. Calculate the fine structure of hydrogen atoms for spin 1 electrons for $n=1$ and $n=2$. Compute the energy shifts in eV.