Abstract
Schrödinger solved the wave equation for the hydrogen atom by considering the moving electron to be described as a three-dimensional wave. By writing the equation in polar coordinates, the separation of variables leads to three equations that can be solved exactly. Two of those equations, the Legendre and Laguerre equations, lead to restrictions on the solutions and give rise to quantum numbers. The Pauli Exclusion Principle leads to the restrictions related to permissible values for n, l, and m. Interpretation of the solutions is given in terms of the probability of finding the electron in regions of space, that is, the s, p, d, … orbitals. The variation method is a procedure for using trial wave functions to calculate properties. The overlap of orbitals on adjacent atoms can lead to the increased probability of finding electrons (bonding), depending on the mathematical nature of the functions.
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