【摘要】 本文考虑了如下的力学系统:其总哈密顿量为H=H_o+V,其中,V为微扰算符,H_o只有连续谱,H除了与之相同的连续谱外,还有相应于束缚态的分立谱。文中证明:相互作用表示的薜定谔方程在无限时刻初条件下的解是不唯一的。但只有一个解是有物理意义的。这个解可以由U(t,±∞)算符作用于初态ψ(±∞)而直接得出,并可作为散射理论的出发点。 其次,借助以上的结果,对Lippmann-Schwinger,Coester以及Arnous-Zienau等人的工作进行了讨论,澄清了其中若干问题。更多还原

【Abstract】 In tins note, we consider a dynamical system of the following type. The total Ilamiltonian H is separated into two parts H0 and V,H0 possesses the same continuous spectrum as that of H, but H possesses in addition a discrete spectrum corresponding to bound states. It is shown that the solution in the interaction representation of the time dependent Schiodinger equation with initial condition specified at t=±∞ is not unique. It contains an unique scattering-state part but an arbitrary bonud -state part. The former part is a physical solution and can be obtained directly by operating U(t,±∞) on initial state ψ(±∞) where U(t,±∞) is defined as lim U(t,t0) (see reference [6]). This solution may be used as thestarting point of formal scattering theory. In addition we have discussed and clarified some points in the earlier works of Lippmann-Schwinger, Greater and Arnous-Zienau.更多还原