We consider the quantized motion of neutral atoms at very low temperature i
n a two-dimensional magnetic quadrupole structure formed, for example, by f
our current-carrying wires along the z direction. The magnetic field B in t
he guide is proportional to the vector (x,-y) We show that this held can be
used to make a single-mode atomic de Broglie waveguide which has bound sta
tes of low angular momentum, even though the field at the center of the gui
de goes to zero. We investigate the spectrum and decay rate of the transver
se modes for spin-1/2 and spin-1 atoms.