Abstract
We have investigated the boundary conditions for the envelope function in the effective mass approximation when the effective mass is position dependent and discontinuous. Under the assumption that the envelope function is discontinuous, we find the boundary conditions that must be imposed on the derivative of the envelope function in order to make the Hamiltonian Hermitian. The standard boundary conditions that are used are found to be a special case of the more general boundary conditions given here. The one-dimensional as well as the three-dimensional case has been investigated.
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