The Luttinger-Kohn canonical transformations are used to derive the effective band Hamiltonian for a quantum well. The transformations produce δ-function potentials in the effective-mass approximation. The boundary conditions on envelope functions, obtained from this effective Hamiltonian, differ from the BenDaniel-Duke ansatz. The effective Hamiltonian depends on the electronic coherence length. It also has a velocity-dependent term that is proportional to the sum of band lineup energies.

• Received 19 July 1993

DOI:https://doi.org/10.1103/PhysRevB.49.7432