Probability representation of quantum evolution and energy level equations for optical tomograms

TL;DR

This paper develops a probability-based framework for quantum evolution using optical tomograms, linking it to known equations and applying it to stationary states and a parametric oscillator example.

Contribution

It introduces a novel probability representation of quantum evolution equations for optical tomograms, connecting them with classical and quantum energy level descriptions.

Findings

Mapped von Neumann and Moyal equations onto optical tomogram evolution equations

Clarified the relation between optical and symplectic tomograms

Derived the classical Liouville equation for optical tomograms

Abstract

The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic tomogram of the quantum state is clarified. The stationary states corresponding to quantum energy levels are associated with the probability representation of the von Neumann and Moyal equations written for the optical tomograms. Classical Liouville equation for optical tomogram is obtained. Example of parametric oscillator is considered in detail.