Multipole expansion of the interaction hamiltonian between a charged particle and a non-uniform magnetic field

Derives a multipole expansion for an interaction hamiltonian for a charged particle moving in a non-uniform static magnetic field. It is shown that the interaction hamiltonian is proportional to the angular momentum as in the case of uniform magnetic field. As a prelude to the final result a means of conversion is established between the scalar potential and the vector potential and multipole expansion of the magnetic vector potential inside a sphere of radius R is obtained.