Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution
Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution
复制标题
二维抛物线陷阱中的三个电子：相对运动解
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
N. Simonović
中科院分区：
文献类型：
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作者：
N. Simonović
摘要：根据科恩定理，二维抛物线陷阱中三个电子的相对运动 (rel) 与质心 (CM) 运动分离。通过引入新的坐标，非相互作用电子近似中相对运动的哈密顿量可以采用标准形式。归一化哈密顿量的本征态是正常模式的福克-达尔文态的产物。相对运动的能级是通过对非相互作用情况的特征基中的精确哈密顿量进行对角化来获得的。在此基础上可以得到解析形式的相互作用矩阵元素。由于哈密顿矩阵的秩显着降低，因此计算速度比完整 (CM + rel) 运动更快、更准确。这一优点对于激发态的计算和能谱的分析尤其重要。
Abstract.In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.