The eight-band k·p-formalism in combination with the second-order continuum elasticity theory has been employed highly successful to understand the elastic and electronic properties of various semiconductor nanostructures like quantum dots, wires and wells. Within the present work, a novel, plane-wave formulation of these two continuum models is presented, which allows to employ these tools with a dramatically increased efficiency to a wide field of nanostructures and a large range of semiconductor materials. A correspondingly wide range of nanostructures that are promising for future application in quantum computing, quantum cryptography or novel light emitting devices, has been investigated in this work. These investigations allow to understand the properties of III-nitride quantum dots, wires and wells grown on polar and nonpolar surfaces that are promising candidates for novel light emitting devices.

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