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Schroedinger's theory of dispersion is applied to the symmetrical top. The dipole of the top is assumed to lie along the axis of symmetry, and the wave-length of the incident light to be large as compared with the dimensions of the top. An explicit expression is derived for the index of refraction of a gas composed of symmetrical tops, as a function of the frequency of the incident light. As the perturbed eigenfunction is a linear function of only 3 unperturbed eigenfunctions, the dispersion formula, for a given state, consists of only 2 terms.The moments for the Raman effect transitions for the symmetrical top are also computed. Simple closed expressions are obtained, again because of the simplicity of the perturbed eigenfunctions. The polarization of the Raman variations is computed with the result that the unshifted lines are unpolarized whereas for the shifted lines: |mz|²|mₓ|²=4/3.
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Morris Muskat (1930) studied this question.
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