On the Sufficiency of the Wavefunction

Martin Ringbauer

Russell Borland, K Dennis

The necessary and sufficient conditions for a one-body reduced density matrix of rank 6 to be derivable from a three-body fermion wavefunction are presented. For this case it can be shown explicitly that the information content of the one-matrix is less than that of the wavefunction. The extension of these conditions to the cases of a three-body function of one-rank 7 and a four-body function of one-rank 8 are also discussed. The authors have obtained sufficient conditions for these two cases. Numerical studies reported in this paper lead us to believe that these conditions are the necessary and sufficient conditions.

S. Rombouts, K. Heyde

A simple necessary and sufficient condition which tells when an A-particle fermion wavefunction can be written as a Slater determinant is proven.

David Z. Albert

Mark S. Ashbaugh

The author presents an elementary example which shows that position and momentum distributions do not uniquely determine the wavefunction. In particular, the example shows that a wavefunction consisting of two gaussian wavepackets with momenta k 1 and k 2 has the same position and momentum distributions as the wavefunction obtained by interchanging k 1 and k 2 . This interpretation relies on viewing the wavefunction as that of a free particle but, of course, the abstract result is simply that for f in L 2 (R) knowledge of mod f(x) mod and mod f(k) mod is not always sufficient to determine f(x) (or f(k); here f denotes the Fourier transform of f). In addition, the bearing of the example presented here upon certain interesting questions raised by Vogt (1978) is discussed.