  We consider the thin layer quantization with use of only the most elementary
notions of differential geometry. We consider this method in higher dimensions
and get an explicit formula for quantum potential. For codimension 1 surfaces
the quantum potential is presented in terms of principal curvatures, and
equivalence with Prokhorov quantization method is proved. It is shown that, in
contrast with original da Costa method, Prokhorov quantization can be
generalized directly to higher codimensions.
