时间相关的多道散射理论

本文把Lippmann-Schwinger等人关于散射理论的时间相关方案扩充到多道情况。Ekstein在1956年也曾试图进行这样的扩充工作。值得特别提到,他所指出并着重引用的事实,即多道情况下的射出(或射入)本征态组的广泛的正交性质,是极为重要的,这是建立散射矩阵概念的基础。但是,Ekstein没有充分利用Lippmann-Schwinger等人的方案所包含的相当普遍的出发点,原方案的简明性没有保留下来。而且由于无法用一个单独的相互作用表示来建立散射算符,就认为散射矩阵不能看作某种线性算符的表示,使散射矩阵的概念含混起来。本文保持原有Lippmann-Schwinger方案的基本精神及简明性而把它扩充为多道理论。给出了散射算符的明显形式。跃迁几率与散射矩阵的关系可以按照单道情形的方法来推导。 关键词：

THE TIME-DEPENDING SCATTERING THEORY OF MULTI-CHANNEL PROCESS

The time-depending formal theory of scattering, initiated by Lippmann and Schwinger is generalized to the case of multi-channel process.Ekstein has attempted to construct such a theory in 1956 and pointed out the orthogonality properties of the set of multi-channel outgoing (incoming) scattering states, which is very important for the establishment of scattering matrix, but it seems to him that the quite general starting point of the L-S formalism is not appreciated. In his work the simplicity of the L-S formalism is lost. He came to the conclusion that the scattering matrix can not be regarded as the matrix of a single linear operator, because he insisted to work in one single interaction representation for all the initial and final states. Thereby the concept of scattering matrix is confused.The present paper deals with the same generalization, but the simplicity of the L-S formalism is preserved. The explicit form of the scattering operator is given. The calculation of the various transition probability in the present case can be made in a similar way as in the original L-S theory.