# Quantum linear response theory

Consider again the Hamiltonian for a system coupled to a time-dependent field

\[H = H_0 - BF_e(t)\]

We wish to solve the quantum Liouville equation

\[i\hbar {\partial \rho \over \partial t} = [H,\rho]\]

in the linear regime where \(F_e(t)\) is small.