Research On Some Basic Theories In PT-symmetric Quantum Theory

In 1998,Bender C.M and Boettcher proposed the PT-symmetry,which refers to symmetry of the system's Hamiltonian H about the Parity-time.and demonstrates that the eigenvalue of complete symmetric Hamiltonian are the real.Besides the eigenvalue of Hermitian operator is real.PT-symmetry motivates the study of many frontier issues,including non-Hermitian operator quantum mechanics,quantum field theory,non-Hermitian Anderson model,open quantum system.Therefore,this the-ory of PT-symmetry has real physical meaning.In this paper,we first introduce the basic theoretical knowledge of PT-symmetry and then give the description of state and the evolution of pure state in the PT-symmetry quantum system.Based on this theory,we discuss the quantum measurement of the PT-symmetry quantum theory.The specifics of the paper are as follows:In chapter 1,we mainly introduce some research status and background on our contents,and list some basic concepts and symbols.In chapter 2,firstly,according to the relationship between the PT-inner product and the original inner product,we characterize the pure state in the PT-symmetry quantum systems,and illustrate it in detail by an example;Secondly,it is obtained the characterization about the mixed state in the PT-symmetry quantum systems.In chapter 3,we mainly study the evolution of state in PT-symmetry quantum systems,and give a necessary and sufficient condition of the unitary evolution result of the state.In chapter 4,we give the general concept of quantum measurement in the PT-symmetry quantum systems.And illustrate it in detail,and we obtain two results about quantum measurement in the PT-symmetry quantum systems.