Time-Dependent Quantum and Ensemble Averages: Initial Preparation of the System

This chapter considers the initial preparation of the many-particle system, whose control is achieved before the reference time t ₀ when the time-dependent perturbation begins to act on the system. After t ₀, the system is let to evolve in time according to the full time-dependent Hamiltonian. The initial control can be either full or partial. Full control signifies that at t ₀ the system is prepared in a definite “pure” quantum state (like the ground state), while partial control signifies that initially the system is only known to be in a “mixture” of states with given probabilities, such that the information on the phases of the superposition is lost. These two cases are here treated separately.