Canonical transforms, quantumness and probability representation of quantum mechanics

TL;DR

This paper introduces a novel quantum state representation based on linear canonical transforms, using probability distributions instead of wave functions, demonstrated through the Moshinsky shutter problem.

Contribution

It develops a tomographic probability framework for quantum states utilizing canonical transforms, offering an alternative to traditional wave function or density matrix descriptions.

Findings

Probability distribution fully determines quantum states

Canonical transforms connect classical and quantum descriptions

Application to Moshinsky shutter problem demonstrates method

Abstract

The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or density matrix. The example of Moshinsky shutter problem is considered.