A quantum form of the Boltzmann equation which applies to a gas of atoms which interact through a potential with an attractive portion is developed. It is shown that the existence of discrete negative eigenvalues of the Hamiltonian describing the relative motion leads to modifications of the usual equation. It is then shown that in the classical limit, the limit in which h goes to zero, the present results lead to the results previously obtained through a discussion in which the modifications which arise from a potential involving an attraction portion were considered from a classical point of view.