Is there any method to solve the many particle stationary scattering problem like the one for the single particle problem?

Question

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.

Comments

If the particles are interacting, this has no answer, because even without a potential the scattering is as complicated as with one. If the particles are only interacting with the potential, the single particle solution generates the many-particle solution through the trivial product states.

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For example, these is no interaction, but the state is entangled. What I want to know is wave function method solved by boundary conditions for many particle state.

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You just write down the entangled in state, and turn it into the entangeled out state. A basis for the scattering states are all the "trivial" products of the scattering solutions for one particle. If the particles are noninteracting, the solution to the one-body problem automatically solves the many body problem.