Solutions of the Schrödinger equation in the case of a semiinfinite crystal

It is proved that the bounded solutions of the Bloch type in $x_1$, $x_2$ variables of the Schrödinger equation with the potential which is periodic in the semi-space $\{x_3\geqslant 0\}$ and exponentially decreases when $x_3\to -\infty$, may be approximated by the solutions of the Schrödinger equation which correspond to crystal films with a number of layers tending to infinity. It gives the possibility to find the number of linearly independent solutions of this type under some propositions.