TY - JOUR
T1 - Towards the explicit computation of Bohm velocities associated to N-electron wave-functions with arbitrary spin-orientations
AU - Alarcón, A.
AU - Cartoixà, X.
AU - Oriols, X.
PY - 2010/11/1
Y1 - 2010/11/1
N2 - 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. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
AB - 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. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
KW - Exchange interactions
KW - Many-particle wave functions
KW - Spin orientations
U2 - https://doi.org/10.1002/pssc.200983841
DO - https://doi.org/10.1002/pssc.200983841
M3 - Article
VL - 7
SP - 2636
EP - 2639
JO - Physica Status Solidi (C) Current Topics in Solid State Physics
JF - Physica Status Solidi (C) Current Topics in Solid State Physics
SN - 1862-6351
ER -