标题： 量子等压非线性振子作为Swanson哈密顿量的厄米共轭和伪超对称性 显示英文标题

标题： Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry

摘要： 在伪超对称的思想中，我们研究了一个非厄米哈密顿量$H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag 2}$，其中$\alpha \neq \beta$和$\xi$是一阶微分算子，以获得伙伴势$V_{+}(x)$和$V_{-}(x)$，它们分别是新的各向同性势和各向同性非线性振荡器，作为非厄米伙伴哈密顿量$H_{\pm}$的厄米等效物。 我们提供了一种代数方法来获得非线性各向同性振荡器的能谱和波函数。 在一些参数限制下获得了$V_{-}(x)$的解，这些解是Swanson哈密顿量的厄米对应物，这些参数限制已被找到。 此外，我们已经验证，如果交织算子满足$\eta_{1} H_{-}=H_{+} \eta_{1}$，其中$\eta_{1}=\rho^{-1} \mathcal{A} \rho$和$\mathcal{A}$是一阶微分算子，它分解了$H_{\pm}$的厄米特等价物。 显示英文摘要

摘要： Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian $H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag 2}$, where $\alpha \neq \beta$ and $\xi$ 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 $\eta_{1} H_{-}=H_{+} \eta_{1}$, where $\eta_{1}=\rho^{-1} \mathcal{A} \rho$ and $\mathcal{A}$ is the first order differential operator, which factorizes Hermitian equivalents of $H_{\pm}$.