Spherical functions special values

The polarization unit vector of a linearly polarized vector plane wave is given by (1.18). If the vector plane wave propagates along the z-axis we have / = a = 0 and for / = 0, the spherical vector harmonics are zero unless m = 1. Using the special values of the angular functions and when (3 = 0,... 

The electron s wave function (iK atomic orbital) is a mathematical description of the electron s wavelike behavior in an atom. Each wave function is associated with one of the atom s allowed energy states. The probability density of finding the electron at a particular location is represented by An electron density diagram and a radial probability distribution plot show how the electron occupies the space near the nucleus for a particular energy level. Three features of an atomic orbital are described by quantum numbers size (n), shape (/), and orientation (m/). Orbitals with the same n and / values constitute a sublevel sublevels with the same n value constitute an energy level. A sublevel with / = 0 has a spherical (s) orbital a sublevel with / = 1 has three, two-lobed (p) orbitals and a sublevel with / = 2 has five, multi-lobed (d) orbitals. In the special case of the H atom, the energy levels depend on the n value only. 

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