A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems
文献类型：期刊论文
| 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 |
| ISSN号 | 1932-6203 |
| 关键词 | PSEUDO-HERMITICITY QUANTUM-MECHANICS FIELD-THEORY OPERATORS SPECTRUM |
| 通讯作者 | Miao, YG (reprint author), Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China. |
| 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. |
| 学科主题 | Physics |
| 资助信息 | 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 | http://dx.doi.org/10.1371/journal.pone.0097107 |
| 语种 | 英语 |
| WOS记录号 | WOS:000338430700008 |
| 公开日期 | 2015-06-03 |
| 源URL | [http://ir.itp.ac.cn/handle/311006/15737]  |
| 专题 | 理论物理研究所_理论物理所1978-2010年知识产出 |
| 推荐引用方式 GB/T 7714 | 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. |
| APA | Li, JQ,Miao, YG,&Xue, Z.(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. |
入库方式： OAI收割
来源：理论物理研究所
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