Energy band rearrangement along a control parameter in isolated molecules is studied through axially symmetric Hamiltonians describing the coupling of two angular momenta \(\mathbf{S}\) and \(\mathbf{L}\) of fixed amplitude. We focus our attention on the case \(S=1\) which, albeit nongeneric, describes the global rearrangement of a system of energy bands between two well-defined limits corresponding to uncoupled and coupled momenta. The redistribution of energy levels between bands is closely related to the degeneracy of the eigenvalues of the corresponding semiquantum Hamiltonian at isolated points of the three-dimensional Cartesian product of the two-dimensional phase space and the one-dimensional control parameter space. The present paper shows that the band rearrangement for the full quantum system can be quantitatively, rather than qualitatively, reproduced with Dirac oscillator approximations. We also interpret the energy band rearrangement by comparing the evolution of the joint spectra of commuting observables (i. e., energy and axial angular momentum) with that of the image of the energy-momentum map of the completely classical limit of the Dirac oscillator approximations.

通过描述对称振幅固定角的两个角动量\（\ mathbf {S} \）和\（\ mathbf {L} \）的耦合的轴向对称哈密顿量研究沿孤立分子中的控制参数进行的能带重排。我们将注意力集中在\（S = 1 \）上尽管不是通用的，但它描述了在两个明确定义的极限之间的能带系统的全局重排，该极限对应于未耦合和耦合的动量。能带之间的能级重新分布与二维相空间和一维控制参数空间的三维笛卡尔积的孤立点处相应半量子哈密顿量的特征值的退化密切相关。本文表明，可以用狄拉克振荡器逼近来定量而不是定性地重现整个量子系统的能带重排。我们还通过比较通勤可观察物的联合光谱的演化来解释能带重排（即，能量和轴向角动量）与Dirac振荡器逼近的完全经典极限的能量动量图的图像。