  In this work, Schr\"odinger and Dirac equations will be examined in
geometries that confine the particles to hypersurfaces. For this purpose, two
methods will be considered. The first method is the thin layer method which
relies on explicit use of geometrical relations and the squeezing of a certain
coordinate of space (or spacetime). The second is Dirac's quantization
procedure involving the modification of canonical quantization making use of
the geometrical constraints. For the Dirac equation, only the first method will
be considered. Lastly, the results of the two methods will be compared and some
notes on the differences between the results will be included.
