TL;DR
This paper introduces a new integral-free approach to Wigner functions for specific wave functions, simplifying their computation using differential operators, with applications to Gaussian and oscillator states.
Contribution
It presents a novel method to define Wigner functions without integrals for wave functions of a certain form, expanding computational techniques in quantum phase space analysis.
Findings
Wigner functions can be expressed via differential operators for specific wave functions.
The method is demonstrated on Gaussian wave packets and harmonic oscillators.
The approach simplifies calculations of Wigner functions in quantum mechanics.
Abstract
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type , the Wigner function can be defined in terms of differential operators acting on a given function, independently from the integral formula which appears in the standard definition. Gaussian wave packet, harmonic and singular oscillators are given as the examples.
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Taxonomy
TopicsQuantum optics and atomic interactions · Optical and Acousto-Optic Technologies · Laser-Matter Interactions and Applications