Study On Matrix In PT Symmetric Quantum System

We mainly study the matrices in PT symmetric quantum system in this paper.The PT symmetry quantum theory was put forward by professor Bender C.M.Bender et al in 1998,which showed that non-Hermitian Hamiltonian posses real eigenvalues provided they respect unbroken PT symmetry.PT symmetry refers to the parity-time symmetry,where P stands for parity and T stands for time reversal.Recently,there has been a great deal of interest in studying PT symmetric quantum theory.In standard quantum mechanics the observable is represented by Hermitian operator,but which governed by non-Hermitian operator in PT symmetric quantum system.The main contents of this paper are as follows:firstly,we introduce the origin and development of PT symmetric matrix and its difference from Hermite matrix in classical quantum mechanics,and some research status of PT symmetric matrix.We also summarize the significance of the contents in this paper.Secondly,the part of preliminary knowledge mainly introduces the basic knowledge and related definitions and theorems,then introduces an important theorem,which present that non-Hermite matrix can be described by two Hermite matrices.Then,on the basis of the concepts of operator P,operator T and PT symmetry,we use the definition of operator T to classify and discuss the operator it and study its influence on PT symmetry.We also discuss the concrete properties and forms of operator P in 2 x 2 system and 3×3 system based on operator T.Especially,based on the known PT symmetric Hamiltonian in 2 x 2 system,and on the premise that the operator T is a complex conjugate operator,we discuss the form of 2 x 2 operator P,and find the concrete form of non-Hermitian Hamiltonian of PT symmetric condition.Thirdly,using the CPT inner product,this paper discusses the CPT entanglement firstly,and then discusses the entanglement of PT symmetric bell States in classical Hermite condition.Finally,the research process and the results are summarized briefly.