Non-oscillating solutions to uncoupled Ermakov systems and the semi-classical limit (Q2766279)

The goal of this paper is to consider the non-oscillating solutions of uncoupled Ermakov systems and the semi-classical limit. The author investigates the amplitude-phase formulation of the Schrödinger equation within the context of uncoupled Ermakov systems, to prove that in the semi-classical \((\hslash\to 0)\) limit, the only non-oscillating solutions are the ones that yield classical quantities: in particular, the only semi-classical phase function that does not oscillate is the classical reduced action and conversely the quantum continuation, \(f\) or \(\hslash\), of the classical reduced action is a non-oscillating function, moreover, some properties of amplitude-phase functions, their behaviour as a function of \(x\) and \(E\) and their connection with Ermakov systems are also discussed.