Mathematical concepts series expansions

The solution of the Schrddinger equation by means of the partitioning technique and the concept of reduced resolvents is then treated. It is shown that the expressions obtained are most conveniently interpreted in terms of inhomogeneous differential equations. A study of the connection with the first approach reveals that the two methods are essentially equivalent, but also that the use of reduced resolvents and inverse operators may give an altemative insight in the mathematical structure of perturbation theory, particularly with respect to the bracketing theorem and the use of power series expansions with a remainder. In conclusion, it is emphasized that the combined use of the two methods provides a simpler and more powerful tool than any one of them taken separately. 

Fig. 8.12. The concept of a MO as a LCAO, a section view. From the point of view of mathematics, it is an expansion in a series of a complete set of functions. From the viewpoint of physics, it is just recognizing that when an electron is close to nucleus a. it should behave in a similar way as that required by the atomic orbital of atom a. From the point of view of a bricklayer, it represents the construction of a large building from soft and mutually interpenetrating bricks.

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