A characteristic feature of a topological material is the existence of unique boundary states that cannot be realized but as the termination of a topological bulk. In a Weyl semi-metal these are given by the surface Fermi-arcs, whose open-contour Fermi-surface curves between pairs of surface projections of bulk Weyl nodes of opposite chirality. We show the visualization of these topological Fermi arc states on the surface of the recently discovered Weyl semi-metal tantalum arsenide (TaAs) probing via scanning tunneling spectroscopy [1]. Its surface hosts 12 Fermi arcs from 24 Weyl nodes alongside several surface bands of non-topological origin. Using the distinct structure and spatial distribution of the wavefunctions associated with the different bands, we detect all possible scattering processes in which Fermi arcs are involved (intra- and inter arc scatterings and arc-trivial scatterings). Each of the measured scattering processes entails information on the unique nature of Fermi arcs in TaAs: their contour, their dispersion and its relation with the Weyl nodes, the relative uniform structure of their Bloch wave function, and their association with tantalum sites which indicates their close relation with the tantalum derived bulk Weyl cones. Unlike trivial surface states, the topological Fermi arc wavefunction is found to be insensitive to the surface potential and spreads uniformly within the unit cell, resembling a plane wave nature. The analysis technique we demonstrate, based on the structure of the Bloch wave function within the unit cell, is applicable to other electronic systems of interest such as high temperature superconductors and topological crystalline insulators.

[1] Science Advances 2, 8, e1600709 (2016)