  The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is
mapped onto a non-interacting Fermi gas with renormalized potential. This is
done by means of flow equations for Hamiltonians and is valid for small
electron-electron interaction. This method also yields an alternative
bosonization formula for the transformed field operator which makes no use of
Klein factors. The two-terminal conductance can then be evaluated using the
Landauer formula. We obtain similar results for infinite systems at finite
temperature by identifying the flow parameter with the inverse squared
temperature in the asymptotic regime. We recover the algebraic behavior of the
conductance obtained by Kane and Fisher in the limit of low temperatures and
weak electron-electron interaction, but our results remain valid for arbitrary
external potential.
