The Lagrangian of an isotropic continuous medium and Lagrangian formalism are used to consistently derive acoustic eigenmodes, to normalize them, and to determine the acoustic phonons (confined acoustic phonons) in a free‐standing quantum well. These phonons may be classified as shear, dilatational, and flexural phonons in accordance with the acoustic terminology for eigenmodes. The Hamiltonians describing interactions of the confined acoustic phonons with electrons in the approximations of the deformation potential and the piezoelectric scattering potential are obtained and analyzed.
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Bannov et al. (1994) studied this question.
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