  The effect of an atomically sharp impenetrable interface on the spin
splitting of the spectrum of two-dimensional electrons in heterostructures
based on (001) III-V compounds has been analyzed. To this end, the single band
Hamiltonian $\Gamma_{6c}$ for envelope functions is supplemented by a general
boundary condition taking into account the possibility of the existence of Tamm
states. This boundary condition also takes into account the spin-orbit
interaction, the asymmetry of a quantum well, and the lack of inversion
symmetry in the crystal and contains the single phenomenological length $R$
characterizing the structure of the interface at atomic scales. The model of a
quasitriangular well created by the electric field $F$ has been considered.
After the unitary transformation to zero boundary conditions, in the modified
Hamiltonian interfacial contribution appears, from which the two-dimensional
spin Hamiltonian is obtained through averaging over the fast motion along the
normal. In the absence of magnetic field $\boldsymbol B$, this contribution is
the sum of the Dresselhaus and the Bychkov-Rashba terms with the constants
renormalized owing to the interfacial contribution. In the field $\boldsymbol
B$ containing the quantizing component $B_z$, the off - diagonal (in cubic
axes) components of the $g$-factor tensor are linear functions of $|B_z|$ and
the number of the Landau level $N$. The results are in qualitative agreement
with the experimental data.
