Abstract
Chemical bonds are not completely rigid. This results in the atoms vibrating about some equilibrium positions. One of the essential quantum mechanical models is that used to describe such vibrations, which are quantized. The basic approach is to make use of a force-distance relationship and to consider the stretching and compression of a bond in terms of a spring. This problem leads to a differential equation known as Hermite's Equation, the solutions of which are the Hermite polynomials. A series of vibrational states of different energy will be populated according to the Boltzmann Distribution Law. Metal atoms in a lattice vibrate about equilibrium positions in a somewhat similar way so the same principles used in discussing vibrations in bonds can be used to derive expressions for the heat capacity of metals.
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