We prove a D=1 analytic versal deformation theorem for WKB expansions. We define the spectrum of an operator in local analytic terms. We use the Morse lemma to show that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.
The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics
Quantum mechanics and classical trajectories
Quantum mechanics of damped systems
