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Hartree's work

The Hartree product is the wave function, which is the product of the wave functions of each of the particles entering the system under consideration separately [1] . The Hartree product implies that the individual particles do not interact and act as an unsymmetrized Slater determinant in the Hartree – Fock method [2] .

For three particles,

Ψ(xone,x2,x3)=χone(xone)χ2(x2)χ3(x3).{\ displaystyle \ Psi (\ mathbf {x} _ {1}, \ mathbf {x} _ {2}, \ mathbf {x} _ {3}) = \ chi _ {1} (\ mathbf {x} _ {1}) \ chi _ {2} (\ mathbf {x} _ {2}) \ chi _ {3} (\ mathbf {x} _ {3}).} {\ displaystyle \ Psi (\ mathbf {x} _ {1}, \ mathbf {x} _ {2}, \ mathbf {x} _ {3}) = \ chi _ {1} (\ mathbf {x} _ {1}) \ chi _ {2} (\ mathbf {x} _ {2}) \ chi _ {3} (\ mathbf {x} _ {3}).}

For fermions, such a description is not appropriate, because the resulting wave function is not antisymmetric [3] [4] . The antisymmetric wave function can be mathematically described by the Slater determinant .

See also

  • Hartree-Fock Method

Notes

  1. S An Introduction to Hartree-Fock Molecular Orbital Theory for C. David Sherrill (2000)
  2. Within within within theory theory theory theory theory theory Je Je Je Je Je 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112, 1150 (2000); https://doi.org/10.1063/1.480669
  3. AM PAM Dirac, The Principles of Quantum Mechanics , 4th edition, Clarendon, Oxford UK, (1958) p. 248
  4. ↑ The Symmetrizer and Antisymmetrizer por John Armstrong (2008)


Source - https://ru.wikipedia.org/w/index.php?title=Product by_hartry&oldid = 96966425


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