The problem of the linear triatomic molecule can be reduced to one of two degrees of freedom by introducing coordinates y1 = x2 − x1, y2 = x3 − x2, and eliminating x2 by requiring that the center of mass remain at rest. Obtain the frequencies of the normal modes in these coordinates and show that they agree with the results of Section 6.4. The distances between the atoms, y1 and y2, are known as internal coordinates.
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