Luttinger liquid in a finite one-dimensional wire with box-like boundary conditions

We study a Luttinger Liquid in a finite one-dimensional wire with box-like boundary conditions by considering the local distribution of the single-particle spectral weight. This corresponds to the experimental probability of extracting a single electron at a given place and energy, which can be interpreted as the square of an electron wave function. For the noninteracting case, this is given by a standing wave at the Fermi wave vector. In the presence of interactions, however, the wave functions obtain additional structure with a sharp depletion near the edges and modulations throughout the wire. In the spinful case, these modulations correspond to the separate spin- and charge-like excitations in the system.