An effective quality factor representing both the interaction between atoms within the atom laser and the quality factor is introduced to study the propagation of the atom laser beam . we derive the abcd formulation of the propagation of an atom laser beam with arbitrary beam profile including the interaction between atoms within the atom laser by means of the theory of quantum mechanics 因此，本章在schrsdinger形式理论的基础上，引入守恒的有效品质因子来讨论有效品质因子守恒的的含时量子系统?原子激光(考虑了原子激光内部原子间相互作用)传播子的有效abco形式。
