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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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An application of representation theory to molecular vibration

Representation theory is used extensively in many of the physical sciences. Such applications come about because every physical system has a symmetry group G, and certain vector spaces associated with the system turn out to be imageG-modules. For example, the vibration of a molecule is governed by various differential equations, and the symmetry group of the molecule acts on the space of solutions of these equations. It is on this application – the theory of molecular vibrations – that we concentrate in this final chapter. In order to keep our treatment elementary, we stay within the ...

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