论文标题
来自能量的波形：简单电位的应用
Wavefunctions from Energies: Applications in simple potentials
论文作者
论文摘要
一个了不起的数学属性 - 以某种方式隐藏并重新发现 - 允许直接从其特征值获得遗传学矩阵的特征向量。这打开了从频谱中获取波形的可能性，这是许多物理领域的难以捉摸的目标。在这里，评估该公式的简单电位，从而恢复了机器精度内的理论波形。该特征值的一个惊人特征 - EigenVector的关系是它不需要知道工作矩阵的任何条目。但是，它需要了解次要矩阵的特征值（其中已从原始矩阵中删除了一行和列）。我们在这些子膜光谱中找到了一种模式，可以分析获得特征向量。分析了这种模式背后隐藏的物理信息。
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the spectrum, an elusive goal of many fields in physics. Here, the formula is assessed for simple potentials, recovering the theoretical wavefunctions within machine accuracy. A striking feature of this eigenvalue--eigenvector relation is that it does not require knowing any of the entries of the working matrix. However, it requires the knowledge of the eigenvalues of the minor matrices (in which a row and a column have been deleted from the original matrix). We found a pattern in these sub-matrices spectra, allowing to get the eigenvectors analytically. The physical information hidden behind this pattern is analyzed.
