Time-dependent momentum expectation values from different quantum probability and flux densities
- 11 February 2021
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 154 (6), 064307
- https://doi.org/10.1063/5.0039466
Abstract
Based on the Ehrenfest theorem, the time-dependent expectation value of a momentum operator can be evaluated equivalently in two ways. The integrals appearing in the expressions are taken over two different functions. In one case, the integrand is the quantum mechanical flux density , and in the other, a different quantity appears, which also has the units of a flux density. The quantum flux density is related to the probability density ρ via the continuity equation, and may as well be used to define a density that fulfills a continuity equation. Employing a model for the coupled dynamics of an electron and a proton, we document the properties of the densities and flux densities. It is shown that although the mean momentum derived from the two quantities is identical, the various functions exhibit a very different coordinate and time-dependence. In particular, it is found that the flux density directly monitors temporal changes in the probability density, and the density carries information about wave packet dispersion occurring in different spatial directions.
Keywords
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