We discuss how cross sections and probabilities for reaction can be calculated quantum mechanically for chemical reactions, based on three examples (two-dimensional model of the gas phase reaction A + BC --> AB + C, photodissociation of a tri-atomic molecule, and the dissociation of a diatomic molecule on a surface).  Subjects include: the scattering boundary conditions, the time-dependent and the time-independent Schrodinger equation, the stationary and the time-dependent wave function, the wave packet method, the choice of the initial wave packet, the propagation of the time-dependent wave function, the representation of the wave function and the action of the Hamiltonian operator on the wave function, and the asymptotic analysis.