I am trying to write down the slater determinant for 10 electron filling from 1s up , 1s down, 2s up, 2s down, 2px up, 2px down, 2py up,2py down, 2pz up, 2pz down, There are totally 10 single particle states, I can write down a 10 x 10 slater determinant. My question here is that whether we can factorize the slater determinant into space part and spin part such that spin part is antisymmetric.
(1)What is the general procedure to factorize the slater determinant?
(2)Can young Tableau help me doing this?
Please suggest some references as well.
This is the same kind of questiin as What is the difference between Gogol and Gegel? Or, between Babel and Bebel? Slater determinant is made by design to account for Pauli principle. Mathematically this is done with help of determinants. Spin part and space part initially separated because Schrodinger equation does not have room for spin at all. Only space part. However with only space part you cannot build a determinant. thus completely artificially spin part is inserted by hand into wave function so that it can beproperly symmetrized or antisymmetrized. use of Dirac equation spares from these artificialities but the formalism is not developed mathematically rigorously sincechemists are not familiar with Clifford algebra. Instead , the second quantization formalism is used. The wave function in this formalism is linear combination of spatial wave functions multiplied by creation- annihilation operators. These are taking care of spin effects
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