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A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems
Li, JQ; Miao, YG; Xue, Z; Miao, YG (reprint author), Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China.
2014
发表期刊PLOS ONE
ISSN1932-6203
卷号9期号:6页码:e97107
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.
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
关键词Pseudo-hermiticity Quantum-mechanics Field-theory Operators Spectrum
学科领域Physics
资助者Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027]
DOI10.1371/journal.pone.0097107
URL查看原文
收录类别SCI
语种英语
资助者Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027] ; Alexander von Humboldt Foundation; National Natural Science Foundation of China [11175090]; Ministry of Education of China [20120031110027]
WOS记录号WOS:000338430700008
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文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/15737
专题理论物理所SCI论文
通讯作者Miao, YG (reprint author), Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China.
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GB/T 7714
Li, JQ,Miao, YG,Xue, Z,et al. A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems[J]. PLOS ONE,2014,9(6):e97107.
APA Li, JQ,Miao, YG,Xue, Z,&Miao, YG .(2014).A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems.PLOS ONE,9(6),e97107.
MLA Li, JQ,et al."A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems".PLOS ONE 9.6(2014):e97107.
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