A Note on the Relation between Potential Terms and Metric Matrices

The purpose of this paper is to introduce representation of kinetic fields in Schrodinger equations and to give the relation between potential terms and metric matrices via general structure of spaces rather than Euclidean spaces. We obtain two results from the point of view in Fourier analysis and pseudodi erential operators. One is the derivation of the potential terms in Schrodinger e quations from the representation of kinetic fields by metric matrices in Schrodinger type equation, the other is the derivation the metric matrices in Schrodinger type equation from the potential terms in Schrodinger equation in the one-dimensional Euclidean space.