Crossed Electric and Magnetic Fields

Here we analyze a J=1 state subject to crossed electric and magnetic fields. The effects of Stark mixing on the sublevels of a single state can be accounted for to second order in the electric field by writing an effective Hamiltonian in terms of the polarizability of the atomic state.

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Define the atomic system. The state is assumed to have a tensor polarizability but no scalar polarizability.
The Hamiltonian for the system subject to the magnetic and electric fields. We must explicitly specify the "Polarizability" interaction, because it is not included by default.
The eigenenergies and eigenstates of the system in the presence of the fields.
An energy plot as a function of electric field for fixed magnetic field.
An energy plot as a function of magnetic field for fixed electric field.