Research On The Generalized Wigner-Yanase Skew Information And The Generalized Schr(o|¨ )dinger Uncertainty Relation

In this paper, from the view of the relationship between operator algebra and quantum mechanics, we research the generalized form of the Schrodinger uncertainty relation by using the operator spectrum theory and the cycle nature of trace, and then establish an uncertainty relation by virtue of the generalized Wigner-Yanase skew information. In addition, we further discuss several intuitive properties and su-peradditivity conjecture of the generalized Wigner-Yanase-Dyson skew information. Finally we give the definition of Vρε(A), Uα,ρ,ε(A) and establish the Schrodinger uncertainty relation in terms of them. Main contents of this paper are summarized as follows:In Chapter 1, we introduce some symbolic representation in quantum mechan-ics, the development of the skew information as well as the importance of uncertainty principle in describing the basic rule of the micro particle movement. Then, we list the main contents of this paper and give several basic definitions which will be needed in the following three chapters.In Chapter 2, we put forward to the definition of the generalized Wigner-Yanase correlation, the generalized covariance and discuss the properties of them. Based on this, we obtain the generalized Schrodinger uncertainty principle described by |Iρ|(A). In addition, we further discuss several intuitive properties of the general-ized Wigner-Yanase-Dyson skew information and the quantitative relation between |Varρο|) and |IP|(A).In Chapter 3, we study the superadditivity conjecture of the generalized Wigner-Yanase-Dyson skew information.In Chapter 4, we introduce several generalized definitions and give some equiva-lent and size relationships between them. We establish the Schrodinger’s uncertainty relation in terms of Vρ,ε(A) and Uaα,ρ,ε(A).