Some Research On Pt-symmetry Quantum Theory

Bender and the collaborators discovered that not every Hamiltonian is Hermi-tian and proposed PT-symmetry in1998. Hereafter, some elementary points of the PT-symmetricity and its mathematical or physical descriptions have been studied and part of the results have been proved. This paper is devoted to researching the PT-symmetric quantum state discrimination and unbroken PT-symmetry on the basis of some existing theories by use of operator theory and matrix theory. The paper is divided into four chapters and the specifics are as follows:In Chapter1, we mainly introduce some research status and background on our contents, and list some notations, the relevant basic concepts and conclusions.In Chapter2, we investigate abstract PT-symmetric theory. PT-symmetric quantum theory is discussed by applying the relevant knowledge of multiplication operator and unitary transformation, some important results and properties are given.In Chapter3, the state-discrimination problem is examined in the context of PT quantum mechanics, based on the fact that a non-Hermitian PT-symmetric Hamiltonian determines the new inner product for the Hilbert space, description of the unambiguous discrimination for the two states｜Ψ1> and｜Ψ2> is given.In Chapter4, PT-symmetry and unbroken PT-symmetry of Hamiltonian H are introduced, the related properties of H having unbroken PT-symmetry are dis-cussed, and an equivalent description of linear operator H is obtained.