Sturmians normalization

Sturmian basis set obeys a potential-weighted orthogonality relationship analogous to equation (10). This still does not tell us how to normalize the functions, and in fact the choice is arbitrary. However, it will be convenient to choose the normalization in such a way that in momentum space the orthonormality relations become ... 

The determinential wave functions shown in equations (42)-(44) have the correct normalization for many-electron Sturmians (i.e. the normalization required by equation (6)). To see this, we can make use of the Slater-Condon rules, which hold for the diagonal matrix elements of... 

If we wish to malce accurate molecular calculations with many-electron Sturmians, we must pay careful attention to the question of normalization Suppose that we wish to find the normalization constant M for the basis function ... 

We must remember that the subscript v represents a set of indices, and the constants jS may be independent of some of them. Orthogonality with respect to these minor indices must be established or constructed in some other way. Assuming that this has been done, we next need to normalize the generalized Sturmian basis set. It turns out that the most natural and convenient choice of normalization is that which yields the potential-weighted orthonormality relations in the form... 

In the case of atomic calculations, this choice of normalization does not need to be imposed. It results spontaneously from the form of the generahzed Sturmian basis set. 

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