  A small change of basis in k.p theory yields a Kane-like Hamiltonian for the
conduction and valence bands of narrow-gap semiconductors that has no spurious
solutions, yet provides an accurate fit to all effective masses. The theory is
shown to work in superlattices by direct comparison with first-principles
density-functional calculations of the valence subband structure. A
reinterpretation of the standard data-fitting procedures used in k.p theory is
also proposed.
