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We present Fourier-space based methods to calculate the electronic structureof wurtzite quantum dot systems with continuous alloy profiles. We incorporatespatially varying elastic and dielectric constants in strain and piezoelectricpotential calculations. A method to incorporate smooth alloy profiles in allaspects of the calculations is presented. We demonstrate our methodology forthe case of a 1D InGaN quantum dot array and show the importance of includingthese spatially varying parameters in the modeling of devices. We demonstratethat convergence of the lowest bound state energies is to good approximationdetermined by the largest wave vector used in constructing the states. We alsopresent a novel approach of coupling strain into the$\mathbf{k}\cdot\mathbf{p}$ Hamiltonian, greatly reducing the computationalcost of generating the Hamiltonian.

Efficient quantum dot $\mathbf{k}\cdot\mathbf{p}$ in wurtzite systems  including spatially varying elastic and dielectric constants and smooth alloy  profile