Wave equation scaled hydrogenic

Acceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the fi eld of quantum mechanics, which examines the wave nature of objects on the atomic scale. In 1926, Erwin Schrddinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom. The model describes an atom that has certain allowed quantities of energy due to the allowed frequencies of an electron whose behavior is wavelike and whose exact location is impossible to know. 

The Schrodinger equation for the D-dimensional analogue of hydrogen (equation (88)) can be solved exactly, both in direct space and in reciprocal space and in both cases the solutions involve hyperspheri-cal harmonics. In this section we shall discuss the close relationship between hyperspherical harmonics, harmonic polynomials, and exact D-dimensional hydrogenlike wave functions. We shall also discuss the importance of these functions in dimensional scaling and in the hyperspherical method. 

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