Continuous Transitions Between Quantum and Classical Motions

TL;DR

This paper demonstrates how a nonlinear Schrödinger equation can model continuous transitions between quantum and classical behaviors across various physical systems, providing insights into the quantum-classical boundary.

Contribution

It introduces a nonlinear Schrödinger framework that unifies quantum and classical motions, applicable to systems like the double-slit, harmonic oscillator, and hydrogen-like atom.

Findings

Continuous quantum-classical transition modeled successfully

Applicable to empirical systems like double-slit and hydrogen atom

Provides a unified nonlinear approach to quantum mechanics

Abstract

Using a nonlinear Schr\"{o}dinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the hydrogen-like atom, all of which are of empirical interest.