  The phenomenological description of propagation of atomic matter waves inside
a curved atom wave guide is presented based on the effective action principle.
The evolutions in both temporal and spatial domains for the atomic matter wave
in the presence of guiding potential fields (classical and quantized) are
considered. The coherent control of three-level atomic matter waves in a wave
guide by an external controlling light is briefly discussed. The concepts of
{\it atomic matter-wave bandgap structure} in a spatially periodic guiding
field ({\it e.g.}, the interior potential of carbon peapod which can trap both
atoms and light) and {\it optical lattice bandgap medium} are suggested.
