Experimental determination of the properties of semiconductor quantum dots is bedevilled by the spread in sizes of dot in the population. Nevertheless, interest in their optical properties and their dependence on the degree of confinement of electrons, holes, and lattice waves has stimulated a considerable literature. In particular, the excitation of electrons and holes, the nature of the exciton, the interaction with phonons, and the anharmonic effects associated with the Stokes shift have received considerable attention. The common approach to the electron-phonon interaction has been via the DC model. This chapter focuses on the confinement of lattice waves and in particular, of polar optical modes and their hybridization. The chapter covers: scalar and vector potentials in spherical coordinates; ionic displacements for LO and TO modes; polar double hybrids; quantum disc and quantum box.
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