Wavefunctions for Non-interacting Electrons

As an important special case, consider the Hamiltonian for N non-interacting electrons  

The eigenfunctions of the one-electron problem of (1.13) and (1.14) are spin orbitals which can be used to construct the antisymmetric eigenfunctions of i non  

As an example, consider the ground state for the non-interacting helium atom N = 2). The occupied spin orbitals are 

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