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Starting from a classical Hamiltonian for nonhomogeneous elastic media, a procedure is developed for acoustic phonon quantization in resonators as well as linear and planar waveguides. The formalism is illustrated in an example of acoustic phonon modes in a buried cylindrical waveguide. The deformation potential Hamiltonian for electron - acoustic phonon interaction is also obtained.
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Stroscio et al. (1996) studied this question.
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