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题名: A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems
作者: Li, JQ ;  Miao, YG ;  Xue, Z
刊名: PLOS ONE
出版日期: 2014
卷号: 9, 期号:6, 页码:e97107
关键词: PSEUDO-HERMITICITY ;  QUANTUM-MECHANICS ;  FIELD-THEORY ;  OPERATORS ;  SPECTRUM
学科分类: Physics
DOI: 10.1371/journal.pone.0097107
通讯作者: Miao, YG (reprint author), Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China.
部门归属: [Li, Jun-Qing ;  Miao, Yan-Gang ;  Xue, Zhao] Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China ;  [Miao, Yan-Gang] Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing, Peoples R China ;  [Miao, Yan-Gang] Univ Bonn, Bethe Ctr Theoret Phys, Bonn, Germany ;  [Miao, Yan-Gang] Univ Bonn, Inst Phys, Bonn, Germany
英文摘要: A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator eta(+) and defining the annihilation and creation operators to be eta(+) -pseudo-Hermitian adjoint to each other. The operator eta(+) represents the eta(+) -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator eta(+) is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.
资助者: Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027]
收录类别: SCI
原文出处: 查看原文
语种: 英语
WOS记录号: WOS:000338430700008
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/15737
Appears in Collections:理论物理所2014年知识产出 _期刊论文

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Recommended Citation:
Li, JQ,Miao, YG,Xue, Z. A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems[J]. PLOS ONE,2014,9(6):e97107.
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