Coefficient of fractional parentage
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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.
- [math]\displaystyle{ \Psi_{1\ldots N}(j^N\alpha JM)= \sum_{\alpha_1 J_1} \langle j^{N-1}(\alpha_1 J_1);j J\mid\} j^N \alpha J \rangle \left[\Psi_{1\ldots N-1}(j^{N-1}\alpha_1 J_1)\otimes \psi_N(j)\right]^J_M }[/math]
The state [math]\displaystyle{ \Psi_{1\ldots N}(j^N\alpha JM) }[/math] is normalized and totally anti-symmetric with respect to permutations of all its N particles, while the state [math]\displaystyle{ \Psi_{1\ldots N-1}(j^{N-1}\alpha_1 J_1) }[/math] is normalized and totally anti-symmetric with respect to all its N − 1 particles.
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![]() | Original source: https://en.wikipedia.org/wiki/Coefficient of fractional parentage.
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