Adiabatic Response to an Oscillatory Field

The behavior of a quantum-mechanical system with a slowly modulated oscillatory Hamiltonian is characterized by an adiabatic theorem similar to that for a system with a slowly changing ``static'' Hamiltonian. Quasiperiodic states—solutions of the instantaneous Schrödinger equation with an oscillatory Hamiltonian—play the same role as eigenfunctions of the instantaneous Hamiltonian do in an adiabatic theorem for a nearly static Hamiltonian. As an example, the theorem is used to establish the correct wavefunction to be used in computing the refractive index of atomic hydrogen.