Some Research On Odd PT-frames

PT-symmetric theory was posed by Professor Bender, University of Wash-ington, in1998. The theory has a real physical background and significance, and received widespread attentions of scholars. This article briefly introduces the basic ideas and methods of PT-symmetry with the mathematical tool. Some briefly promotion of the previous conclusions are discussed by using operator algebra and matrix method, the structure and properties of non-Hermitian Hamilton operator H with PT-symmetry and unbroken PT-symmetry are explored under the conditions that T2=1and T2=-1, respectively. For a non-Hermitian Hamilton operator H with PT-symmetry, a new Hilbert space is obtained by building a right inner product. 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 basic concepts.In chapter2, firstly, some basic concepts such as PT-structure and PT-sym-metry are introduced. Secondly, we introduce momentum operator and multiplica-tion operator, the structure and properties of the non-Hermitian Hamilton operator with PT-symmetry under specific parity and time reversal are given by using the matrix method in the end of this part.In chapter3, we first introduce a new time evolution. T2=-1and the odd PT-frame. Next, we define PT-symmetry under the time evolution, and some of their properties is studied. Furthermore, we can’t define the unbroken PT-symmetry like T2=1under the new time evolution T2=-1.In chapter4, we first introduce the definition of the unbroken PT-symmetry under the odd PT-frame and discussed the eigenvalues. Next, we give the definition of PT-inner product and CPT-inner product and discuss the properties, two examples are given.