- Calculate the energy shifts to the four hyperfine
ground states of hydrogen in a weak magnetic field. (The
field is weak enough so that the perturbation is smaller than
the hyperfine splitting.)
- Calculate the splitting for the ground state of positronium due to the spin-spin interaction between the electron and the positron. Try to correctly use the reduced mass where required but don't let this detail keep you from working the problem.
- A muonic hydrogen atom (proton plus muon) is in a
relative state in an external magnetic field.
Assume that the perturbation due to the hyperfine interaction and
the magnetic field is given by
.
Calculate the energies of the four nearly degenerate ground
states.
Do not assume that any terms in the Hamiltonian are small.
- A hydrogen atom in the ground state is put in a magnetic field.
Assume that the energy shift due to the B field is of the same order
as the hyperfine splitting of the ground state.
Find the eigenenergies of the (four) ground states as a function of the B field strength.
Make sure you define any constants (like ) you use in terms of fundamental constants.

Jim Branson 2013-04-22