N-Representability Problem for Fermion Density Matrices. I. The Second-Order Density Matrix with N =3

The N representability problem is the problem of how to recognize whether a given pth-order reduced density matrix is derivable from an antisymmetaic N-particle wavefunction ψ by integrating out all but coordinates from ψ*ψ. The conditions under which a given second-order density matrix is N representable by a three-particle wavefunction are discussed.