Investigation of PT-symmetric Hamiltonian Systems from an Alternative Point of View

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 counterp...

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Bibliographic Details
Published in:理论物理通讯：英文版 2012, Vol.58 (10), p.497-503
Main Author: 李军青 李倩 缪炎刚
Format: Article
Language:English
Subjects:
Hilbert空间
代数方法
哈密顿系统
埃尔米特
对称系统
希尔伯特空间
操作员
量子力学
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Summary: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.
ISSN:0253-6102