Mitas Lubos
Department of Physics and CHiPS, North Carolina State University, Raleigh, North Carolina 27695, USA.
Phys Rev Lett. 2006 Jun 23;96(24):240402. doi: 10.1103/PhysRevLett.96.240402.
We study nodes of fermionic ground state wave functions. For two dimensions and higher we prove that spin-polarized, noninteracting fermions in a harmonic well have two nodal cells for arbitrary system size. The result extends to noninteracting or mean-field models in other geometries and to Hartree-Fock atomic states. Spin-unpolarized noninteracting states have multiple nodal cells; however, interactions and many-body correlations generally relax the multiple cells to the minimal number of two. With some conditions, this is proved for interacting two and higher dimensions harmonic fermion systems of arbitrary size using the Bardeen-Cooper-Schrieffer variational wave function.
我们研究费米子基态波函数的节点。对于二维及更高维度，我们证明了在谐振子阱中自旋极化的非相互作用费米子，对于任意系统尺寸都有两个节点单元。该结果扩展到其他几何结构中的非相互作用或平均场模型以及哈特里 - 福克原子态。自旋非极化的非相互作用态有多个节点单元；然而，相互作用和多体关联通常会将多个单元松弛到最少的两个。在某些条件下，使用巴丁 - 库珀 - 施里弗变分波函数对任意尺寸的二维及更高维相互作用谐振子费米子系统证明了这一点。
