Collect. Czech. Chem. Commun. 2011, 76, 399-406
Published online 2011-04-07 13:34:46

Two uncertainty relations

Lubomír Skálaa,b,* and Vojtěch Kapsaa

a Charles University in Prague, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Czech Republic
b University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1


Heisenberg and Robertson–Schrödinger uncertainty relations for the coordinate and momentum follow from two stronger uncertainty relations. The first uncertainty relation has classical character and its right-hand side can have an arbitrary value greater than or equal to zero. The second uncertainty relation has quantum character and its right-hand side equals h2/4; its existence is related to the existence of the envelop of the wave function. These two uncertainty relations cannot be obviously improved on. The equality sign in the second relation can be achieved for much larger class of the wave functions than in case of the Heisenberg or Robertson–Schrödinger uncertainty relations.

Keywords: Uncertainty relations; Heisenberg and Robertson–Schrödinger uncertainty relations; Fisher information.

References: 19 live references.