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In Sect. 4.2 we saw how the 3 rN equations of motion of a periodic solid can be largely decoupled by means of the plane-wave ansatz and the assumption of harmonic forces. With (4.7) we arrived at a system of equations that, for a given wave vector q, couples the wave amplitudes of the atoms within a unit cell. It can be shown mathematically that within the harmonic approximation the equations of motion, even for a nonperiodic solid, can be completely decoupled by means of a linear coordinate transformation to so-called normal coordinates. We thereby obtain a total of 3 rN independent forms of motion of the crystal, each with a harmonic time dependence and a specific frequency which, in the case of a periodic solid, is given by the dispersion relation ω(q). Any one of these “normal modes” can gain or lose energy independently of the others.
KeywordsSpecific Heat Capacity Harmonic Approximation Anharmonic Oscillator Thermal Current Radiation Shield
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