It can be seen that the use of Slater determinants ensures an antisymmetrized function at the outset; other functions are automatically rejected.
32.
To this end, it is assumed that the total wavefunction ( the Slater determinant ) is such that the energy is minimum.
33.
This classification allows one to develop a set of Slater determinants for the description of the wavefunction as a linear combination of these determinants.
34.
Tasks are nucleus : each task difficulty has an order of hierarchical complexity required to complete it correctly, analogous to the atomic Slater determinant.
35.
The rules are used in deriving the working equations for all methods of approximately solving the Schr�dinger equation that employ wavefunctions constructed from Slater determinants.
36.
The second step consists in assuming that the wavefunction of the system can be written as a Slater determinant of one-particle spin-orbitals.
37.
Once you satisfy that condition, ( for instance using a Slater determinant ) then you can have two electrons with opposite spin in the same spatial orbital.
38.
It is inherently mean-field ( assumes the particles are independent ) and is the unsymmetrized version of the Slater determinant ansatz in the Hartree Fock method.
39.
It was then shown that a Slater determinant, a determinant of one-particle orbitals first used by Heisenberg and Dirac in 1926, trivially satisfies the exchange.
40.
The linear combination of Hartree products for the two-particle case can clearly be seen as identical with the Slater determinant for " N " = 2.
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