  A geometric potential $V_C$ depending on the mean and Gaussian curvatures of
a surface $\Sigma$ arises when confining a particle initially in a
three-dimensional space $\Omega$ onto $\Sigma$ when the particle Hamiltonian
$H_\Omega$ is taken proportional to the Laplacian $L$ on $\Omega$. In this work
rather than assume $H_\Omega \propto L$, momenta $P_\eta$ Hermitian over
$\Omega$ are constructed and used to derive an alternate Hamiltonian $H_\eta$.
The procedure leading to $V_C$, when performed with $H_\eta$, is shown to yield
$V_C = 0$. To obtain a measure of the difference between the two approaches,
numerical results are presented for a toroidal model.
