Heisenberg's uncertainty relation gets stronger

Qiu-Cheng Song, Cong‐Feng Qiao

Vishnu M. Bannur

Recently, Maccone and Pati [Phys. Rev. Lett. {\bf 113}, 260401 (2014)] derived few inequalities among variances of incompatible operators which they called stronger uncertainty relations, stronger than Heisenberg-Robertson or Schrodinger uncertainty relations. Here we generalize their study to get infinite number of such inequalities and propose that only one of them may be the correct uncertainty relation between incompatible operators. We get back well known uncertainty relations of Heisenberg-Robertson and Schrodinger under certain limits. We also reexamine the conclusions of Maccone and Pati and comment on their work.

R. Shankar

Lubomír Skála, V. Kapsa

Abstract Two uncertainty relations, one related to the probability density current and the other one related to the probability density, are derived and discussed. Both relations are stronger than the Heisenberg uncertainty relations. Their generalization to the multidimensional case and to the mixed states is also discussed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

R. Shankar