Weights of nonorthogonal functions

The probability interpretation of the wave function in quantum mechanics obtained by forming the square of its magnitude leads naturally to a simple idea for the weights of constituent parts of the wave function when it is written as a linear combination of orthonormal functions. Thus, if 

each of the has a certain physical interpretation or significance, then one says the wave function or the state represented by it, consists of a fraction 

NB We assumed this not to happen in our discussion above of the convergence in the linear variation problem. 

No such simple result is available for nonorthogonal bases, such as our VB functions, because, although they are normalized, they are not mutually orthogonal. Thus, instead of Eq. (1.42), we would have 

In Section 2.8 we discuss some simple functions used to represent the H2 molecule. We choose one involving six basis functions to illustrate the various methods. The overlap matrix for the basis is 

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Weights of nonorthogonal functions elements equal to 1. We write it in partitioned form as... 

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