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Hartree product (Read 4163 times)
Gerrit-Jan Linker
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Hartree product
17.05.08 at 19:12:34
 
Hartree product
 
ψHP(r1,r2,...,rN)=Ф1(r12(r2)...ФN(rN)
 
ψHP is called the Hartree product. It is a N electron wavefunction used to describe the system.
Фi is a spatial orbital i
ri 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: ψH(r1H(r2).
 
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:
ψHP(x1,x2,...,xN)=χ1(x12(x2)...χN(xN)
 
Here xi denote the spatial coordinates ri of electron one and its spin coordinate (with value either alpha or beta)
χi denotes spin orbital i which consists of a spatial part Фi and a spin function. So if electon i has alpha spin you get the spin ortial χi = Фiα  
 
A Hartree product does not satisfy the antisymmetry principle. See the topic on the anti-symmetry principle for more information.
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« Last Edit: 25.02.11 at 21:29:15 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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