The effect of band mixing and non-parabolicity on quantum well gain and spontaneous emission is studied using k.p theory. Spectra of gain and spontaneous emission are strongly modified but the relation of maximum gain versus nominal current density is not strongly affected.
M. F. H. Schuurmans,
"Band Mixing And Quantum Well Gain", Proc. SPIE 0792, Quantum Well and Superlattice Physics, (11 August 1987); doi: 10.1117/12.940855; https://doi.org/10.1117/12.940855