Linear Combinations of Wave Functions

The first allowable equation holds for bosons, and the second holds for femiions. If we form a linear combination of wave functions for bosons. 

Such a wave function is represented by a linear combination of wave functions for more than one electron configuration, and is called a "multi-configurational" wave function. The consideration of more than one configuration can reduce the correlation error. Such an approach is referred to as the method of configuration interaction (Cl) . 

In most cases one chooses as the variational function a linear combination of wave functions which are correct to a certain approximation, for example, for large nuclear separations. In this case we choose (see below) 0 = cx(pL + r29n. 

In solving problems in this book, we shall not obtain wave functions by solving differential equations such as Eq. (1-5), but shall instead assume that the wave functions that interest us can be written in terms of a small number of known functions. For example, to obtain the wave function ij/ for one electron in a diatomic molecule, we can make a linear combination of wave functions j/i and l/2, where 1 and 2 designate energy eigenstates for electrons in the separate atoms that make up the molecule. Thus,... 

The wave functions forming the basis of the irreducible representations, can be represented in the form of a linear combination of wave functions tpj obtained by solving Schrodin-ger s equation for a centrally symmetric field ... 

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