Non-oscillating solutions to uncoupled Ermakov systems and the semiclassical limit

Abstract

The amplitude-phase formulation of the Schrödinger equation is investigated within the context of uncoupled Ermakov systems, whereby the amplitude function is given by the auxiliary nonlinear equation. The classical limit of the amplitude and phase functions is analyzed by setting up a semiclassical Ermakov system. In this limit, it is shown that classical quantities, such as the classical probability amplitude and the reduced action, are obtained only when the semiclassical amplitude and the accumulated phase are non-oscillating functions respectively of the space and energy variables. Conversely, among the infinitely many arbitrary exact quantum amplitude and phase functions corresponding to a given wavefunction, only the non-oscillating ones yield classical quantities in the limit $\hslash \to 0$.

2 figures

References in corpus (1)

• On the linearization of the generalized Ermakov systems

Cited by in corpus (6)

• Generalized Hamiltonian structures for Ermakov systems
• Entanglement in the classical limit: quantum correlations from classical probabilities
• Realism and the wave-function
• Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over paths
• On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group
• Quantum and semiclassical phase functions for the quantization of symmetric oscillators