  This is the first of a series of papers to construct the deformation theory
of the form Schr\"odinger equation, which is related to a section-bundle system
$(M,g,f)$, where $(M,g)$ is a noncompact complete K\"ahler manifold with
bounded geometry and $f$ is a holomorphic function defined on $M$.
  This work is also the first step attempting to understand the whole
Landau-Ginzburg B-model including the higher genus invariants. Our work is
mainly based on the pioneer work of Cecotti, Cecotti and Vafa
\cite{Ce1,Ce2,CV}.
