Stark Effect in Resonant Rotating Wave
Let us consider the atom of Hydrogen in the electric field rotating with a constant angular frequency and the Hamilton operator
where the unperturbed Hamiltonian is
- ,
and the perturbation is one of the space coordinates
The has the meaning of the electric field and is the operator of the component of the angular momentum.
The eigenvalues of are
For the lowest eigenstates of Hydrogen, and in the resonance they are therefore both equal, while the eigenstates are different. The eigenvalue equation takes the form
where
which leads to the quadratic equation which can be readily solved
with the solution
Those are Stark states in the rotating frame so-called Trojan (higher eigenvalue) and anti-Trojan wavepackets.
Read more about this topic: Perturbation Theory, Example of Degenerate Perturbation Theory
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