The driven oscillator

TL;DR

This paper uses phase space methods to analyze the quantum harmonic oscillator under external white noise and time-dependent parameters, deriving exact transition probabilities and effects on phase variables.

Contribution

It provides exact solutions for transition probabilities and noise effects in a quantum harmonic oscillator with external driving, using the Wigner-Weyl phase space approach.

Findings

Exact transition probabilities for driven quantum oscillators

Analysis of white noise effects on phase variables

Insights into quantum noise influence on harmonic oscillators

Abstract

Using the Wigner-Weyl mapping of quantum mechanics to phase space we consider exactly the quantum mechanics of an harmonic oscillator driven by an external white noise force or whose frequency is time dependent, either adiabatically or parametrically. We find several transition probabilities exactly. We also consider the (quantum mechanical) randomizing effects of the external white noise force on the Weyl quantized phase angle and upon other Weyl quantized quantities.