Operator antisymmetrisation

It might be desirable, therefore, to use physical and chemical knowledge to set up a trial form for an approximate wavefunction which is more appropriate to the problem. If we set up such a model wavefunction we can ensure that it satisfies the Pauli principle by applying the antisymmetrising operator A. Notice that, if a wavefunction is already antisymmetric, application of A docs not change it ... 

To see that this is true it is only necessary to write out each full permutation operator in the definition of the antisymmetrising operator explicitly as a product of a spatial permutation and a spin permutation ... 

In fact, it is useful to think of the process of obtaining a determinant from a simple spin-orbital product as the result of an operator acting on that product. If we define the antisymmetrising operator A, say, by... 

A is here an antisymmetrisation operator. For the excited state in which one molecule na is excited and aU the others remain in their ground states, the wavefunction... 

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