  The ballistic conductance of a coupled $T$-shaped semiconductor quantum wire
(CTQW) are studied. Two types of CTQW are considered, one of which is a $\Pi
$-shaped quantum wire ($\Pi $QW) which consists of two transverse wires on the
same side of the main wire and the other a $\Pi $-clone quantum wire ($\Pi
$CQW) which consists of two transverse wires on the opposite sides of the main
wire. The mode matching method and Landauer-Buttiker theory are employed to
study the energy dependence of the ballistic conductance. Most of transmission
profiles of $\Pi $QW and $\Pi $CQW are found to be distinguishable for large
separation $d$ between the two transverse arms. The transmission probability
manifests oscillatory behavior when $d$ is increased. When a potential is added
to the connection region, it results in decoupling or coupling effects between
the two T-shaped wires according to whether it is positive or negative. When
magnetic fields are applied to CTQW, the transmission profiles are found to be
affected profoundly even if the electrons pass through the field free region
only.
