  The surface Hamiltonian for a spin zero particle that is pinned to a surface
by letting the thickness of a layer surrounding the surface go to zero --
assuming a strong normal force -- is constructed. The new approach we follow to
achieve this is to start with an expression for the 3D momentum operators whose
components along the surface and the normal to the surface are separately
Hermitian. The normal part of the kinetic energy operator is a Hermitian
operator in this case. When this operator is dropped and the thickness of the
layer is set to zero, one automatically gets the Hermitian surface Hamiltonian
that contains the geometric potential term as expected. Hamiltonians for both a
neutral and a charged particle in an electromagnetic field are constructed. We
show that a Hermitian surface and normal momenta emerge automatically once one
symmetrizes the usual normal and surface momentum operators. The present
approach makes it manifest that the geometrical potential originates from the
term that is added to the surface momentum operator to render it Hermitian;
this term itself emerges from symmetrization/ordering of differential momentum
operators in curvilinear coordinates. We investigate the connection between
this approach and the similar approach of Jenssen and Koppe and Costa ( the so
called Thin-Layer Quantization (TLQ)). We note that the critical transformation
of the wavefunction introduced there before taking the thickness of the layer
to zero actually -- while not noted explicitly stated by the authors -- renders
each of the surface and normal kinetic energy operators Hermitian by itself,
which is just what our approach does from the onset.
