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Li, JQ; Miao, YG; Xue, Z; Miao, YG (reprint author), Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China.
A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems
Source PublicationPLOS ONE
Language英语
KeywordPseudo-hermiticity Quantum-mechanics Field-theory Operators Spectrum
AbstractA 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.
2014
ISSN1932-6203
Volume9Issue:6Pages:e97107
Subject AreaPhysics
DOI10.1371/journal.pone.0097107
Indexed BySCI
Funding OrganizationAlexander 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]
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Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/15737
Collection理论物理所科研产出_SCI论文
Corresponding AuthorMiao, YG (reprint author), Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China.
Recommended Citation
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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