一维和三维谐振子约束下自旋极化费米子的非发散赝势处理
Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement
摘要：
利用零程δ函数势成功地模拟了玻色一维原子的原子-原子散射，利用Fermi-Huang正则化s波赝势成功地模拟了玻色三维原子的原子-原子散射.在这里，我们推导出两个自旋极化的一维费米子在外部谐波约束下通过零程势相互作用的本征能量，它只作用于奇宇称波函数，解析。我们还提出了一个无发散的零程势处理两个自旋极化的三维费米子在谐波约束。我们的赝势处理方法通过数值计算短程模型势进行了验证。
英文摘要：
Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zero-range delta-function potential, while that of bosonic 3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave pseudo-potential. Here, we derive the eigenenergies of two spin-polarized 1D fermions under external harmonic confinement interacting through a zero-range potential, which only acts on odd-parity wave functions, analytically. We also present a divergent-free zero-range potential treatment of two spin-polarized 3D fermions under harmonic confinement. Our pseudo-potential treatments are verified through numerical calculations for short-range model potentials.
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