非厄米哈密顿量的时间无关摄动理论

IF 1.7 4区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

International Journal of Theoretical Physics Pub Date : 2025-09-16 DOI:10.1007/s10773-025-06121-3

Ye-Xin Li, Gui-Xiang La, Gong-Ping Zheng

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引用次数: 0

摘要

将量子力学中厄米哈密顿量的时间无关摄动理论推广到非厄米哈密顿量。文中详细分析了其推导过程。加入了文献中丢失的一些项，得到了一个精确完备的非厄米时无关微扰理论。本文采用另一种方法，即在无扰动哈密顿量的希尔伯特空间中对扰动哈密顿量进行精确对角化，求解了两个说明性的两能级非厄米哈密顿量的本征能量和本征态的修正，分别具有厄米和非厄米无扰动哈密顿量。所得结果与非厄米时间无关微扰理论的结果一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Time-independent Perturbation Theory of Non-Hermitian Hamiltonian

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.

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来源期刊

International Journal of Theoretical Physics 物理-物理：综合

CiteScore

2.50

自引率

21.40%

发文量

258

审稿时长

3.3 months

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.