Coefficient of fractional parentage - Alchetron, the free social encyclopedia

In physics, coefficients of fractional parentage (cfp's) can be used to obtain anti-symmetric many-body states for like particles. In a jj-coupling scheme they are defined by the following relation.

Ψ 1 … N ( j N α J M ) = ∑ α 1 J 1 ⟨ j N − 1 ( α 1 J 1 ) ; j J ∣ } j N α J ⟩ [ Ψ 1 … N − 1 ( j N − 1 α 1 J 1 ) ⊗ ψ N ( j ) ] M J

The state Ψ 1 … N ( j N α J M ) is normalized and totally anti-symmetric with respect to permutations of all its N particles, while the state Ψ 1 … N − 1 ( j N − 1 α 1 J 1 ) is normalized and totally anti-symmetric with respect to all its N − 1 particles.

References

Coefficient of fractional parentage Wikipedia

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