A Class of Quantum States with Classical-like Evolution

TL;DR

This paper introduces a new class of quantum states derived via Nelson stochastic quantization that evolve classically with constant dispersion, extending harmonic oscillator coherent states to more general potentials.

Contribution

It derives exact non-stationary states for time-dependent potentials, broadening the scope of classical-like quantum states beyond harmonic oscillators.

Findings

Wave-packets follow classical trajectories with constant dispersion.

Extension of harmonic-oscillator coherent states to more general potentials.

Explicit example provided with a sextic oscillator potential.

Abstract

In the framework of Nelson stochastic quantization we derive exact non-stationary states for a class of time-dependent potentials. The wave-packets follow a classical motion with constant dispersion. The new states thus define a possible extension of the harmonic-oscillator coherent states to more general potentials. As an explicit example we give a detailed treatement of a sestic oscillator potential.