The negative flow of probability
Issue Date
4-2020
Abstract
We derive an inequality that the parameters of a 1D free-particle Gaussian wave packet with a positive group velocity, approaching a given region x > q, must satisfy such that a negative probability current J exists on q. Local probability conservation implies the counter-intuitive result that the particle detection probability in the region x > q is actually decreasing. The condition J < 0 requires the negative correlation of the position and momentum observables of the state, but the time scales for the negative current and anti-correlation regimes are not identical. Using a probability current operator, we obtain an integral representation of J in momentum space for any free particle wave packet. We use this integral representation to distinguish the separate contributions to J by the positive and negative momentum components, and we identify a third contribution to J composed of cross-terms of both momenta. For the specific case of a Gaussian wave packet with a negative correlation between its position and momentum, the positive momentum component can contribute a negative value to the probability current.
Source or Periodical Title
American Journal of Physics
ISSN
0002-9505
Volume
88
Page
325-333
Document Type
Article
Physical Description
figures; graphs; tables; references
Language
English
Recommended Citation
Villanueva, A.A.D. (2020). The negative flow of probability. American Journal of Physics 88, 325-333. https://doi.org/10.1119/10.0000856
Identifier
https://doi.org/10.1119/10.0000856
Digital Copy
yes