Reduction to a One-Body Problem

In this chapter we show that the spectral analysis of a generalized N-body operator H near a two-cluster threshold can be reduced to the analysis of a one-body operator with a non-linear spectral parameter. Recall that the minimal Conditions 2.3 and 2.4 are always imposed for H. Of course such reduction would not be needed for the one-body problem; however, we recall that throughout our work we impose the condition \(N\ge 2\) .