Heisenberg And Schrödinger Have Several Inequalities In Uncertain Relations

In quantum mechanics,Heisenberg and Schrodinger uncertainty relation is a very important relationship,which has been widely used in many fields.The tradi-tional uncertainty relations are all about the self adjoint operators,and the Heisen-berg and Schrodinger uncertainty relation about general bounded linear operators on Hilbert spaces are also studied by some scholars.According to the previous re-sults,this paper will introduce the concept of generalized symmetric variance and generalized symmetric correlation coefficient by the tracial positive linear maps be-tween C*-algebras.Then we will get the generalized Heisenberg and Schrodinger uncertainty relation and some associated inequalities.The main contents are as follows:In Chapter 1,we mainly introduces some commonly used symbols and concepts.For example,trace preserving mapping,φ-density element,generalized symmetric skew variance,generalized symmetric correlation coefficient and so on.In Chapter 2,we mainly study several inequalities about the Heisenberg and Schrodinger uncertainty relation of the general element on the C*-algebra under the tracial conditional expectation.Let A is a C*-algebra,B is a C*-subalgebra of A,and ε:A→ B is a tracial conditional expectation,in the first section,we mainly prove that if A,B∈A,ρ∈A is a,ε-density element,then V_ρ,ε⁰（A）V_ρ,ε⁰（B）≥（1/4）|ε（ρ[A,B]⁰）|²＋1/4|ε(ρ（ρ{A₀,B₀}⁰）|².in the secend section,we mainly prove that if A,B ∈,A,ρ ∈A is a e-density element,then|Re（|Corrρ,εα|（A,B））|2≤|Iρ,εα|（B）,|Uρ,ε|（A）Uρ,ε（B）≥（1/4）|ε（ρ[A,B]⁰）|².In Chapter 3,we mainly study the Heisenberg and Schrodinger uncertainty relation of the general element on the C*-algebra under the tracial positive linear maps.Let A is a C*-algebra,B is a C*-subalgebra of A,and φ:A→ B is a tracial positive linear map,if A,B∈A,ρ∈ A is a φ-density element,φ（A）is a commutator subspace of B,then Vρ,φ0（A）Vρ,φ0（B）-|Re(Covρ,φ0（A*,B）2≥1/4|φ（ρ[A,B]0）|2.If A,B ∈A,ρ∈ A is a φ-density element such that sp(-iρ^1/2[A,B]⁰ρ^1/2)（?）[m,M],for some scalers 0<m<M,then（?）...