任意自旋取向N电子波函数玻姆速度的显式计算
Towards the explicit computation of Bohm velocities associated to N-electron wave-functions with arbitrary spin-orientations
摘要：
多粒子薛定谔方程的直接解对于非常少的电子是无法计算的。为了超越这一限制，作者之一[X. Oriols，Phys. Rev. Lett. 2007，98（066803）]最近提出了一个新的模型来研究电子-电子关联从玻姆轨迹与时间相关的波包解的伪单粒子薛定谔方程。在上述论文中，假设所有电子具有相同的自旋取向，仅考虑轨道交换相互作用。然后，多粒子波函数是单粒子波包的复斯莱特行列式。本文将以前的形式扩展到研究电子具有不同自旋取向的多粒子波函数，用含时波包处理N个不同电子自旋取向的主要困难是必须研究所有可能的N！N！N！自旋状态之间的排列的产物。为了克服这一计算上难以实现的问题，本文将总波函数视为两个多粒子波函数的分离产物，第一个是自旋向上的，第二个是自旋向下的。为了数值证明这种近似，玻姆速度在不同的反对称的总波函数的情况下计算。计算结果证实了我们的近似在大量情况下的准确有效性。
英文摘要：
The direct solution of the many-particle Schrödinger equation is computationally inaccessible for more than very few electrons. In order to surpass this limitation, one of the authors [X. Oriols, Phys. Rev. Lett. 2007, 98 (066803)] has recently proposed a new model to study electron-electron correlations from Bohm trajectories associated to time-dependent wave-packets solutions of pseudo single-particle Schrödinger equations. In the aforementioned paper only the orbital exchange interaction is considered assuming that all electrons have the same spin orientation. Then, the many-particle wave function is a complex Slater determinant of the single-particle wave-packets. In the present work the previous formalism is extended to study many-particle wave functions where the electrons have different spin orientations.The main difficulty to treat N different electron spin orientations with time-dependent wave-packets is that one must study all the possible N!N! products of permutations among spin states. To overcome this computationally inaccessible problem, in this article the total wave function is treated as a separated product of two many-particle wave functions, the first with spin up and the second with spin down. In order to numerically justify this approximation, the Bohm velocity in different antisymmetric total wave-function scenarios is computed. The computational results confirms the accurate validity of our approximation under a large number of cases.
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