# Some properties of a non-negative quantum-mechanical distribution function

## Document Type

Article

## Publication Date

9-21-1981

## Abstract

We consider the distribution function obtained by smoothing the original distribution function, defined in an earlier publication, with a ground-state harmonic oscillator wave function. We derive its time dependence and show that, in particular, the field-free result does not correspond to the classical result. We point out that the non-negative property of the smoothed function follows immediately from the fact that the integral of the product of two of the original distribution functions is equal, except for a factor2π h {combining short stroke overlay}, to the transition probability between the two states they represent. © 1981.

## Publication Source (Journal or Book title)

Physics Letters A

## First Page

121

## Last Page

126

## Recommended Citation

O'Connell, R., & Wigner, E.
(1981). Some properties of a non-negative quantum-mechanical distribution function.* Physics Letters A**, 85* (3), 121-126.
https://doi.org/10.1016/0375-9601(81)90881-1