  We construct the Hermitian Schr\"{o}dinger Hamiltonian of spin-less as well
as the gauge-covariant Pauli Hamiltonian of spin one-half particles in a
magnetic field that are confined to cylindrical and spherical surfaces. The
approach does not require the use of involved differential-geometrical methods
and is intuitive and physical, relying on the general requirements of Hermicity
and gauge-covariance. The surfaces are embedded in the full three-dimensional
space and confinement to the surfaces is achieved by strong radial potentials.
We identify the Hermitian and gauge-covariant (in the presence of a magnetic
field) physical radial momentum in each case and set it to zero upon
confinement to the surfaces . The resulting surface Hamiltonians are seen to be
automatically Hermitian and gauge-covariant. The well-known geometrical kinetic
energy also emerges naturally.
