论文标题
一维Schrödinger方程的相位空间传播和稳定性分析，用于寻找旋转激发的绑定和共振状态h $ _2 $
Phase-space propagation and stability analysis of the 1-dimensional Schrödinger equation for finding bound and resonance states of rotationally excited H$_2$
论文作者
论文摘要
使用1维schrödinger方程的数学相空间表示，以获得旋转激发h $ _2 $分子的结合和共振状态。分析了相空间切线场的结构，并与在经典允许和禁止区域中波动函数的行为有关。在此相空间表示中，界面的行为像不稳定的轨道一样，共振状态的行为与渐近稳定的周期相似。计算了H $ _2 $的能量摩托图量子的晶格，从而可以将能量作为量子数的函数具有全局视图。作为能量的函数，相位空间轨迹的弧长和绕组数用于获得h $ _2 $的结合和共振状态的能量特征值
A mathematical phase-space representation of the 1-dimensional Schrödinger equation is employed to obtain bound and resonance states of the rotationally excited H$_2$ molecule. The structure of the phase-space tangent field is analyzed and related to the behavior of the wave function in classically allowed and forbidden regions. In this phase-space representation, bound states behave like unstable orbits meanwhile resonance states behave similarly to asymptotically stable cycles. The lattice of quantum states of the energy-momentum diagram for H$_2$ is calculated allowing to have a global view of the energy as function of the quantum numbers. The arc length and winding number of the phase-space trajectories, as functions of the energy, are used to obtain the energy eigenvalues of bound and resonance states of H$_2$
