量子保序非线性振子作为Swanson哈密顿量的厄米对应物和伪超对称性
Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
摘要：
在伪超对称的思想下，我们研究了一个非厄米哈密顿量$H_{-}=ω(ξ^† ξ+\1/2)+αξ^{2}+βξ^{†2}$，其中$α\neq β$和$ξ$是一阶微分算子，得到了作为非厄米哈密顿量$H_{\pm}$的厄米等价的伙伴势$V_{+}(x)$和$V_{-}(x)$，它们分别是新的保序和保序非线性振子.本文提供了一种代数方法来获得非线性同调振子的谱和波函数。在已知的参数限制下，得到了Swanson哈密顿量的Hermitian对应$V_{-}(x)$的解，并检验了纠缠算子是否满足$η_{1} H_{-}=H_{+} η_{1}$，其中$η_{1}=ρ^{-1} \mathcal{A} ρ$和$\mathcal{A}$是分解$H_{\pm}$的Hermitian等价的一阶微分算子.
英文摘要：
Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian $H_{-}=ω(ξ^† ξ+\1/2)+αξ^{2}+βξ^{†2}$, where $α\neq β$ and $ξ$ is a first order differential operator, to obtain the partner potentials $V_{+}(x)$ and $V_{-}(x)$ which are new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian equivalents of the non-Hermitian partner Hamiltonians $H_{\pm}$. We have provided an algebraic way to obtain the spectrum and wavefunctions of a nonlinear isotonic oscillator. The solutions of $V_{-}(x)$ which are Hermitian counterparts of Swanson Hamiltonian are obtained under some parameter restrictions that are found. Also, we have checked that if the intertwining operator satisfies $η_{1} H_{-}=H_{+} η_{1}$, where $η_{1}=ρ^{-1} \mathcal{A} ρ$ and $\mathcal{A}$ is the first order differential operator, which factorizes Hermitian equivalents of $H_{\pm}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
