; Chen, Shu
; Wang, Yupeng] Chinese Acad Sci, Inst Phys, Beijing 100080, Peoples R China
; [Ma, Zhong-Qi] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for an arbitrary confining potential. The eigenfunctions are constructed by the combination of Girardeau's hard-core contacting boundary condition and group theoretical method, which guarantees the obtained states to be simultaneously the eigenstates of S and S(z) and satisfy antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.