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,?-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 ?:A? B is a tracial conditional expectation,in the first section,we mainly prove that if A,B?A,??A is a,?-density element,then V_?,?⁰?A?V_?,?⁰?B???1/4?|???[A,B]⁰?|²?1/4|?(???{A₀,B₀}⁰?|².in the secend section,we mainly prove that if A,B ?,A,? ?A is a e-density element,then|Re?|Corr?,??|?A,B??|2?|I?,??|?B?,|U?,?|?A?U?,??B???1/4?|???[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 ?:A? B is a tracial positive linear map,if A,B?A,?? A is a ?-density element,??A?is a commutator subspace of B,then V?,?0?A?V?,?0?B?-|Re(Cov?,?0?A*,B?2?1/4|???[A,B]0?|2.If A,B ?A,?? A is a ?-density element such that sp(-i?^1/2[A,B]⁰?^1/2)???[m,M],for some scalers 0<m<M,then???...