The stationary scattering problem by a potential barrier lies in every textbook of quantum mechanics, in which the scattering amplitudes for the single particle wave can be obtained by solving the boundary conditions. I wonder is there any similar method for the many particle wave functions scattered by a potential by solving the boundary conditions? For the many particle scattering problem, the scattering amplitudes should describe the scattering between different many particle states. Let me make this question nontrivial by restricting that the many particle wave function should not be direct product states, or they are entangled.