The Driven-Oscillator Evolution in the Tomografic-Probability Representation

TL;DR

This paper explores the evolution of driven harmonic oscillators within the quantum tomographic-probability framework, providing explicit forms for certain states and analyzing the evolution equations and propagators.

Contribution

It introduces explicit tomographic-probability distributions for specific oscillator states and studies the evolution equations and propagators in the tomographic representation.

Findings

Explicit tomograms for coherent and excited states derived

Evolution equations for classical and quantum oscillators analyzed

Tomographic propagator studied in detail

Abstract

We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and squeezed reference frames in the system's phase space. For some specific oscillator states like coherent states and nth excited states, the tomographic-probability distributions (called the state tomograms) are found in an explicit form. The evolution equation for the tomograms is discussed for the classical and quantum driven oscillators, and the tomographic propagator for this equation is studied.