Non-hermitian extensions of Heisenberg type and Schrödinger type uncertainty relations

In quantum mechanics it is well known that the Heisenberg-Schrödinger uncertainty relations hold for two non-commutative observables and density operator. Recently Dou and Du (J. Math. Phys. 54:103508, 2013 ; Int. J. Theor. Phys. 53:952-958, 2014 ) obtained several uncertainty relations for two non-...

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Bibliographic Details
Published in:Journal of inequalities and applications 2015-12, Vol.2015 (1), p.1-9, Article 381
Main Authors: Yanagi, Kenjiro, Sekikawa, Kohei
Format: Article
Language:English
Subjects:
Adjustment
Analysis
Applications of Mathematics
Correlation analysis
Density
Inequalities
Mathematics
Mathematics and Statistics
Operators
Quantum mechanics
Schroedinger equation
Uncertainty
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Summary:In quantum mechanics it is well known that the Heisenberg-Schrödinger uncertainty relations hold for two non-commutative observables and density operator. Recently Dou and Du (J. Math. Phys. 54:103508, 2013 ; Int. J. Theor. Phys. 53:952-958, 2014 ) obtained several uncertainty relations for two non-commutative non-hermitian observables and density operators. In this paper, we show that their results can be given as corollaries of our non-hermitian extensions of Heisenberg type or Schrödinger type uncertainty relations for the generalized metric adjusted skew information or generalized metric adjusted correlation measures which were obtained in Furuichi and Yanagi (J. Math. Anal. Appl. 388:1147-1156, 2012 ).
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-015-0895-x