{"title":"Time-independent Perturbation Theory of Non-Hermitian Hamiltonian","authors":"Ye-Xin Li, Gui-Xiang La, Gong-Ping Zheng","doi":"10.1007/s10773-025-06121-3","DOIUrl":null,"url":null,"abstract":"<div><p>The time-independent perturbation theory of Hermitian Hamiltonian in quantum mechanics is extended to the non-Hermitian Hamiltonian. The derivation procedure is given analytically and in detail. Some terms lost in literatures are added and an exact and complete non-Hermitian time-independent perturbation theory is obtained. The corrections of eigenenergies and eigenstates of two illustrative two-level non-Hermitian Hamiltonians, which have the Hermitian and non-Hermitian unperturbed Hamiltonian, respectively, are solved by another method, namely, the exactly-diagonalizing of the perturbed Hamiltonian in the Hilbert space of the unperturbed Hamiltonian. The results agree well with those from the non-Hermitian time-independent perturbation theory.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 10","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10773-025-06121-3","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The time-independent perturbation theory of Hermitian Hamiltonian in quantum mechanics is extended to the non-Hermitian Hamiltonian. The derivation procedure is given analytically and in detail. Some terms lost in literatures are added and an exact and complete non-Hermitian time-independent perturbation theory is obtained. The corrections of eigenenergies and eigenstates of two illustrative two-level non-Hermitian Hamiltonians, which have the Hermitian and non-Hermitian unperturbed Hamiltonian, respectively, are solved by another method, namely, the exactly-diagonalizing of the perturbed Hamiltonian in the Hilbert space of the unperturbed Hamiltonian. The results agree well with those from the non-Hermitian time-independent perturbation theory.
期刊介绍：
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.
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