Nondivergent pseudopotential treatment of spin-polarized fermions under one- and three-dimensional harmonic confinement

摘要: Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zero-range $\ensuremath{\delta}$-function potential, while that 3D Fermi-Huang's regularized $s$-wave pseudopotential. Here, we derive the eigenenergies two spin-polarized 1D fermions under external harmonic confinement interacting through which only acts on odd-parity wave functions, analytically. We also present divergent-free potential treatment confinement. Our pseudopotential treatments are verified numerical calculations for short-range model potentials.