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

Journal of inequalities and applications

Kenjiro Yanagi¹ 

关键词: trace inequality;    metric adjusted skew information;    non-hermitian observable;    15A45;    47A63;    94A17;   

DOI  :  10.1186/s13660-015-0895-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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).

【 授权许可】

CC BY