Investigation of P T-symmetric Hamiltonian Systems from an Alternative Point of View  

作　　者：李军青 李倩 缪炎刚 

机构地区：[1]School of Physics,Nankai University

出　　处：《Communications in Theoretical Physics》2012年第10期497-503,共7页理论物理通讯（英文版）

基　　金：Supported in part by the National Natural Science Foundation of China under Grant No. 11175090;the Fundamental Research Funds for the Central Universities under Grant No. 65030021

摘　　要：Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones.Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart,this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged.In order to give the positive definite inner product for the PT-symmetric systems,a new operator V,instead of C,can be introduced.The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics,however,it can be constructed,as an advantage,directly in terms of Hamiltonians.The spectra of the two non-Hermitian PT-symmetric systems are obtained,which coincide with that given in literature,and in particular,the Hilbert spaces associated with positive definite inner products are worked out.

关 键 词：PT symmetry positive definite inner product algebraic method 

分 类 号：O413.1[理学—理论物理]