Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

TL;DR

This paper reformulates quantum dynamics using a complex nonlinear Riccati equation, highlighting how initial conditions influence quantum uncertainties in conservative systems with quadratic Hamiltonians.

Contribution

It introduces a novel Riccati equation approach to analyze quantum evolution, emphasizing initial condition sensitivity in Gaussian wave packet systems.

Findings

Quantum uncertainties are highly sensitive to initial conditions.

The Riccati equation provides an alternative framework for quantum dynamics.

Exact solutions are demonstrated for Gaussian wave packets in quadratic systems.

Abstract

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.