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A note on the quantum Hamiltonian for a free particle

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>3/06/1991
<mark>Journal</mark>Physics Letters A
Issue number1-2
Volume156
Number of pages4
Pages (from-to)1-4
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We consider the non-relativistic quantum mechanics of a free particle on a Riemannian manifold and offer an argument for an invariant quantum Hamiltonian proportional to the Laplacian amended by one quarter of the scalar curvature of the manifold. An explicit ordering of the arbitrary canonical variables in the classical Hamiltonian is found that implies the existence of a quantum potential that can be made to vanish at any point by adopting geodesic coordinates for that region of the manifold.