Surface distortion effects on quantum dot helium

The Schrodinger equation for a quantum mechanical particle constrained to a surface includes a potential term dependent on surface curvature. We use differential forms to derive this term and employ Monge representations for two surfaces to obtain specific expressions for the potential. We calculate the first order perturbative effect of this potential on the ground state energy of model quantum dot helium. We find that the energy shift can be sensitive to the detailed shape of the surface distortion. This dependence arises from the Coulomb repulsion between the electron pair, which causes each electron to preferentially sample (or not sample) regions where physical curvature leads to comparatively large values of the distortion potential. (C) 1999 Elsevier Science B.V. All rights reserved.