Single-particle properties in an exactly solvable $A$-body system

A recent theorem states that for quantum many-body systems with short-range interactions the following property holds: the single-particle overlap functions, spectroscopic factors and separation energies of bound eigenstates of the (A-1)(A-1)-particle system are fully determined by the one-body density matrix of the AA-particle system in its ground state. We confirm this property, by explicit construction, for the case of a schematic, exactly solvable system.