Exact envelope-function theory versus symmetrized Hamiltonian for quantum wires: a comparison

We study the influence of shape, orientation, size and material system on the band structure of quantum wires with special attention given to the differences between results obtained with the Burt–Foreman and the Luttinger–Kohn Hamiltonians. We also show how to derive the Hamiltonians for an arbitrary orientation. We find that the difference is independent of the shape and orientation of the quantum wire, but it does depend on the size and the material system chosen. A brief discussion of the results in terms of group theory is provided.