  Many shape analysis methods treat the geometry of an object as a metric space
that can be captured by the Laplace-Beltrami operator. In this paper, we
propose to adapt the classical Hamiltonian operator from quantum mechanics to
the field of shape analysis. To this end we study the addition of a potential
function to the Laplacian as a generator for dual spaces in which shape
processing is performed. We present a general optimization approach for solving
variational problems involving the basis defined by the Hamiltonian using
perturbation theory for its eigenvectors. The suggested operator is shown to
produce better functional spaces to operate with, as demonstrated on different
shape analysis tasks.
