  We present a comprehensive, analytical treatment of the finite Kitaev chain
for arbitrary chemical potential. We derive the momentum quantization
conditions and present exact analytical formulae for the resulting energy
spectrum and eigenstate wave functions, encompassing boundary and bulk states.
In accordance with an analysis based on the winding number topological
invariant, and as expected from the bulk-edge correspondence, the boundary
states are topological in nature. They can have zero, exponentially small or
even finite energy. A numerical analysis confirms their robustness against
disorder.
