  We explore the theory of electrons confined by one dimensional power law
potentials. We calculate the density profile in the high density electron gas,
the low density Wigner crystal, and the intermediate regime. We extract the
momentum space wavefunction of the electron at the Fermi surface, which can be
measured in experiments on tunneling between parallel wires. The onset of
localization leads to a dramatic broadening of the momentum space wavefunction
together with pronounced sharpening (in energy) of the tunneling spectrum.
