In the last chapter we studied how to find approximately the energy eigenstates and eigenvalues of a system whose Hamiltonian is of the form H0 + V, where V is “small” and time independent. Let us now consider a somewhat different situation. Suppose that we begin with a system whose Hamiltonian is H0, and then we proceed to act on the system with a time-dependent external force, describable by an interaction term Vt added to the Hamiltonian. The question is, what effect does the force have on the system? For example, we might shine light on an atom, and ask what are the chances that the light ionizes the atom. Or we might apply a voltage to a piece of metal, and ask how much current is produced.