**Hartree product** ψ

_{HP}(

**r**_{1},

**r**_{2},...,

**r**_{N})=Ф

_{1}(

**r**_{1})Ф

_{2}(

**r**_{2})...Ф

_{N}(

**r**_{N})

ψ

_{HP} is called the Hartree product. It is a N electron wavefunction used to describe the system.

Ф

_{i} is a spatial orbital i

**r**_{i} are the spatial coordinates of electron i

The idea to use a hartree product as a wavefunction to describe the system is going back to the simpelest atom, Hydrogen, which has only one electron. When introducing another electron in Hydrogen to obtain H

^{-} and assuming the electrons do not interact the wavefunction describing that system would be the product of two Hydrogen wavefunctions: ψ

_{H}(

**r**_{1})ψ

_{H}(

**r**_{2}).

The assumption that the two electrons do not interact is a pretty crude assumption... See also the topic on the

independent particle model If we include spin as a coordinate we can write:

ψ

_{HP}(

**x**_{1},

**x**_{2},...,

**x**_{N})=χ

_{1}(

**x**_{1})χ

_{2}(

**x**_{2})...χ

_{N}(

**x**_{N})

Here

**x**_{i} denote the spatial coordinates

**r**_{i} of electron one and its spin coordinate (with value either alpha or beta)

χ

_{i} denotes spin orbital i which consists of a spatial part Ф

_{i} and a spin function. So if electon i has alpha spin you get the spin ortial χ

_{i} = Ф

_{i}α

A Hartree product does not satisfy the antisymmetry principle. See the topic on the

anti-symmetry principle for more information.