Hartree Ansatz Method: Fermion Antisymmetry & Product vs. Linear Combination

[cotyledon]

How does the Hartree product not reflect the antisymmertic nature of Fermions? Why do you take a product rather than a linear combination of the basis functions to get the total wave function (a la LCAO method, i.e. Linear Combination of Atomic Orbitals)?

 

[alxm]

How does the Hartree product not reflect the antisymmertic nature of Fermions?

This is answered in every textbook on the topic. It's also completely obvious if you know what the antisymmetry requirement is.

Why do you take a product rather than a linear combination of the basis functions to get the total wave function (a la LCAO method, i.e. Linear Combination of Atomic Orbitals)?

What makes you think that the linear combination doesn't include products?