金属团簇的形变谐振子与Balian-Bloch理论
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
摘要：
利用量子群技术对具有对称性Uq（3）$\supset$ SOq（3）的三维q变形谐振子（3D q-HO）的金属团簇壳层结构的预言，与Balian和Bloch的周期轨道理论对电子在球腔中运动的限制进行了比较.结果表明，这两个模型的预测之间的协议是建立通过引入一个额外的长期的哈密顿量的3D q-HO，这并不影响超壳的预测。这个项保留了Uq（3）$\supset$ SOq（3）对称性，同时它还可以通过变分过程导出，类似于通过引入变频振荡器（VFO）的概念从通常的谐振子导出莫尔斯振荡器的过程。
英文摘要：
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
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