Exact solution for infinitely strongly interacting Fermi gases in tight waveguides

We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for arbitrary confining potential. The eigenfunctions are constructed by the combination of Gireardeau'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 fulfill the 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.