  We propose an implementation of external homogeneous magnetic fields in
k$\cdot$p Hamiltonians for holes in heterostructures, in which we made use of
the minimal coupling prior to introduce the envelope function approximation.
Illustrative calculations for holes in InGaAs quantum dot molecules show that
the proposed Hamiltonian outperforms standard Luttinger model [Physical Review
102, 1030 (1956)] describing the experimentally observed magnetic response. The
present implementation culminates our previous proposal [Phys. Rev. B 82,
155307 (2010)].
