Quantum Mechanics in Riemannian Manifold. II

Abstract

We have previously argued about the quantum mechanics on the hypersurface VN-1 embedded in Euclidean space RN. We generalize the formalism to the case of VL embedded in Euclidean space RN with 1 ≦L ≪ N. The result is essentially the same as the previous one and the additional term proportional to \hbar2 appears in the potential energy which is related to the extrinsic mean curvature of VL in RN.