Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs

Abstract We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include one-dimensional time-independent Schrödinger equation. Notably, our results are valid both case generic trajectories as well closed trajectories. also explain what sense formal form a basis. As corollary proof, we establish Borel summability large class problems, derive explicit formula transform.