发表机构
Università di Palermo; I.N.F.N., Sezione di Napoli; AGH University, Kraków（巴勒莫大学; 意大利国家核物理研究所那不勒斯分部; 克拉科夫AGH科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一方法处理谐振子、反转谐振子及Berry-Keating哈密顿量，确定其离散谱与本征态，并视为$\mathfrak{su}(1,1)$及其广义版本的生成元。
AI 中文摘要
我们提出了一种统一视角，来审视量子力学中广泛研究的三个著名二次型哈密顿量，即谐振子、反转谐振子以及Berry-Keating哈密顿量。我们描述了一种统一的方法来确定这些算子的离散谱，并推导它们的（广义）本征态。我们还将这些哈密顿量视为$\mathfrak{su}(1,1)$的生成元，以及在存在非厄米生成元时相关的广义版本的生成元。
英文摘要
We propose an unified view to three well known quadratic Hamiltonians widely considered in quantum mechanics, i.e. those of the harmonic oscillator, of the inverted harmonic oscillator, and the Berry-Keating Hamiltonian. We describe an unified approach to determine the discrete spectrum of these operators, and to deduce their (generalized) eigenstates. We also look at these Hamiltonians as the generators of $\mathfrak{su}(1,1)$, and of a generalized version of it relevant in presence of non Hermitian generators.
CommentsA slightly different version is accepted in Journal of Mathematical Physics
