论文标题
斯旺森式的哈密顿量和倒谐波振荡器
A Swanson-like Hamiltonian and the inverted harmonic oscillator
论文作者
论文摘要
我们推断出与Swanson Hamiltonian密切相关的参数依赖性汉密尔顿$H_θ$的特征值和特征向量，我们为其构建了双方态状态。之后，我们展示了如何和从何种意义上说，可以从$h_θ$的倒数量子谐波振荡器的hamiltonian $ h $ h $中。我们表明，正如其他作者建议的那样，无需使用一些临时度量操作员引入不同的标量产品。确实，我们证明了分配方法足以应对倒置振荡器的汉密尔顿$ h $。
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_θ$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the eigensystem of the Hamiltonian $H$ of the inverted quantum harmonic oscillator can be deduced from that of $H_θ$. We show that there is no need to introduce a different scalar product using some ad hoc metric operator, as suggested by other authors. Indeed we prove that a distributional approach is sufficient to deal with the Hamiltonian $H$ of the inverted oscillator.
