Wave equation anti-symmetrical

Spin is not included explicitly in the Hartree calculation and the wave functions are therefore not antisymmetric as required. If anti-symmetrized orbitals are used a set of differential equations... 

While the two equations look similar, in Equation 1.12 a stands for the four quantum numbers n, I, mi and m, which describe the state of each i of the N electrons. These permutate to generate equally valid states following Pauli s exclusion principle, to yield anti-symmetric wave functions in the central field, which are solutions to the Schrodinger equation (Equation 1.4). 

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