04132010b - Quantum Mechanics: The Hydrogen Atom 12th April...

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Unformatted text preview: Quantum Mechanics: The Hydrogen Atom 12th April 2010 I. The Hydrogen Atom Wavefunctions: Orbital Building Blocks 1 The Radial Function Lets consider s- , p- , and d- type orbitals and arrive at some general descriptions of the spatial variation of these functions. If we consider Figure 20.6 in Engel and Reid, we note some qualities of the various wavefunctions (which we will now consider interchangeably as orbitals ). Keep in mind that the x-axis is a reduced distance, but consider it a distance from the nucleus at R = 0. The figure shows the Radial part of the wavefunction: H-atom orbitals have a complex radial and angular dependence that is best discerned via 3-D visualizations; for the present purposes we consider various 2-D representations s- orbitals are non-zero at R = 0. p- orbitals and d- orbitals are zero at R = 0. They have nodal points; in fact in 3-D space (where these functions live) they have nodal planes . s-orbitals have spherical nodal surfaces ....
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04132010b - Quantum Mechanics: The Hydrogen Atom 12th April...

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