论文标题
$ \ Mathcal {Pt} $的超对称性 - 对称的Tridiagonal Hamiltonians
Supersymmetry of $\mathcal{PT}$- symmetric tridiagonal Hamiltonians
论文作者
论文摘要
我们将对超对称三角形的汉顿人的研究扩展到具有真实或复杂的共轭特征值的非热汉密尔顿人的案例。我们在给定的基础上找到了非富米汉尔顿$ H $ untypersmmetric合作伙伴$ h^{+} $之间的矩阵元素之间的关系。此外，可以在内核多项式的帮助下从$ h^{+} $中附加到$ h^{+} $的本征态扩展问题的正交多项式。除了其一般性外，这项工作中发达的形式主义是使用数值强大的高斯正交技术来探测某些物理量的性质（例如$ \ Mathcal {pt} $对称复杂的电位）的自然家园。最后，我们解决了转移的$ \ Mathcal {pt} $ - 对称的摩尔斯振荡器，正好在三角形表示中。
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its supersymmetric partner $H^{+}$ in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to $H^{+}$ can be recovered from those polynomials arising from the same problem for $H$ with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of $\mathcal{PT}$-symmetric complex potentials. Finally, we solve the shifted $\mathcal{PT}$-symmetric Morse oscillator exactly in the tridiagonal representation.
