The wavefunction when antiparallel spin electrons coincide and its relation to the ground-state electron density in the Hookean atom

For a specific force constant, the spatial form of the ground-state wavefun ction Psi(r(1),r(2)) is known analytically for the Hookean atom in which tw o electrons repel coulombically. Hen, it is first shown that the wavefuncti on Psi(r,r) for the antiparallel spin electrons at the same position r is s ufficient to construct the ground-state density in this model example. An o ff-diagonal generalization is then effected, which relates the one-particle density matrix to the electron pair correlation function, again for this s ame model. (C) 2000 Elsevier Science B.V. All rights reserved.