Hyperspherical Harmonics and Generalized Sturmians

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Hyperspherical Harmonics and Generalized Sturmians

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However, it was soon realized that unless the continuum is included, a set of hydrogenlike orbitals is not complete. To remedy this defect, Shull and Lowdin [] - troduced sets of radial functions n Angular Momentum Theory for Diatomic Molecules, R R method of trees, 3 construct the wave functions of more complicated systems for ex- ple many electron atoms or molecules. To remedy this defect, Shull and Lowdin [] - troduced sets of radial functions which could be expressed in terms of Laguerre polynomials multiplied by exponential factors.

The sets were constructed in such a way as to be complete, i.


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Later Rotenberg [, ] gave the name "Sturmian" to basis sets of this type in order to emp- size their connection with Sturm-Liouville theory. There is a large and rapidly-growing literature on Sturmian basis functions; and selections from this literature are cited in the bibliography.

L21.1 Associated Legendre functions and spherical harmonics.

In , Goscinski [] completed a study ofthe properties ofSt- rnian basis sets, formulating the problem in such a way as to make generalization of the concept very easy. In the present text, we shall follow Goscinski's easily generalizable definition of Sturmians.

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