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Contents 1. Introduction . 2. Theory for polariton modes . 2.1. The Helmholtz equations for the polariton modes. 2.2. Solutions of the polariton mode equations 2.3. The properties of the polariton modes, 2.4. An alternative choice of the boundary conditions . 2.5. Optical properties . 3. Theory for pure phonon modes 3.1. The equations for phonons in finite samples 3.2. Examples . 3.3. Optical properties of small samples 3.4. Complex cubic crystals . 3.5. Uniaxial crystals . 4. Infrared absorption (experimental) . 4.1. Experimental work on powdered samples 4.2. Experimental work on cylinders and slabs 5.1. Raman scattering .

In 1937 the Jahn-Teller (JT) effect addressed the instability (potential or actual) of non-linear symmetric molecules with degenerate orbital electronic states. In view of the large variety of JT activity that has taken place since then, we might broaden our perspective to look at works whose subjects fall under the more general heading of "Strong interactions between two dissimilar systems" (where one system is usually bosonic and the other fermionic). In these intervening years we find several highly important works in Physics and Chemistry that come under this heading and were either connected with, or arose from, JT systems, problems and approaches. Apart from high temperature superconductors, we mention Yang-Mills gauge-forces, symmetry breaking (in elementary particles), conical intersections in molecular potential surfaces, surface crossings between them in chemical reactions, entanglements in the quantum theory of measurements and Berry phases. We elaborate on the last two topics. We show first that the slow evolution of a T coupling from the weak to strong regime can model the quantum mechanical three-state measurement situation, when the positions of the nuclei acts as the measuring device. We then employ recently derived integral relations between component moduli and phases in a time dependent wave-function to demonstrate the equivalence between the state-reduction and the phase decoherence interpretations of the measurement process.

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