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Physical Review A

Internal structure of the Heisenberg and Robertson-Schrödinger uncertainty relations: Multidimensional generalization

Lubomír Skála

Published Oct 24, 2013• 6 citations
Publisher

Abstract

It is known that the Heisenberg and Robertson-Schr\"odinger uncertainty relations can be replaced by sharper relations in which the ``classical'' (depending on the gradient of the phase of the wave function) and ``quantum'' (depending on the gradient of the envelope of the wave function) parts of the variances $\ensuremath{\langle}{(\ensuremath{\Delta}x)}^{2}\ensuremath{\rangle}$ and $\ensuremath{\langle}{(\ensuremath{\Delta}p)}^{2}\ensuremath{\rangle}$ are separated. In this paper, multidimensional generalization of these relations is discussed.

DOI
10.1103/physreva.88.042118

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