  A scheme to reduce translational noninvariant quasi-one-dimensional wave
guides into singly or multiply connected one-dimensional (1D) lines is
proposed. It is meant to simplify the analysis of wave guides, with the
low-energy properties of the guides preserved. Guides comprising
uniform-cross-sectional sections and discontinuities such as bends and
branching junctions are considered. The uniform sections are treated as 1D
lines, and the discontinuities are described by equations sets connecting the
wave functions on the lines. The procedures to derive the equations and to
solve reduced systems are illustrated by examples, and the scheme is found to
apply when the discontinuities are distant and the energy is low. When the
scheme applies, it may substantially simplify the analysis of a wave guide, and
hence the scheme may find uses in the study of related problems, such as
quantum wire networks.
