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This thesis is concerned with theoretical calculations of the properties of electronic bound states in semiconductor heterostructures. The complex band structure empirical pseudopotential method (EPM) is used as the foundation of the work. Spin orbit coupling and strain effects (due to lattice mismatch) are included in familiar ways, as is the transfer matrix method, allowing the study of arbitrarily configured heterostructures. These techniques are used to investigate the unusually deep InAs/AlSb conduction band well. The strong possibility of intraband transitions at electro magnetic wavelengths around 1.55µm is predicted, with corresponding enhanced momentum matrix elements and joint density of states over interband transitions. An InAs/GaSb/AlSb asymmetric well is investigated, paying particular attention to the bound states in the vicinity of the InAs/GaSb band overlap. The electron-like states are found to cross with heavy hole and anti-cross with light hole-like states, as a function of heterostructure dimension or applied electrostatic field. This is analogous to the hybridisation of states in the in-plane band structure, except that for zero in-plane wave vector there can be no appreciable hybridisation of electron and heavy hole states. A technique is described that has been developed to extract envelope functions from heterostructure wavefunctions calculated using the realistic complex band structure EPM approach. These envelope functions conform to Burt’s theory (M. G. Burt, J. Phys.: Condens. Matt. 4, 6651 (1992)) in that they are uniquely defined, continuous and smooth over all space. Comparisons with traditional effective mass envelope functions are made. The extracted envelope functions are used to demonstrate conclusively Burt's predictions (M. G. Burt, Superlatt. Mi- crostruct. 17, 335 (1995)) concerning the inadequacy of certain approximations for the calculation of interband dipole matrix elements and charge oscillation. Finally, the issue of k • p operator ordering is convincingly settled, in favour of 'ordered' over 'symmetrised' Hamiltonians, by comparison to EPM calculations, and using EPM derived k • p parameters.