  We present a detailed analysis of continuous time quantum walks (CTQW) with
both position and transition defects defined at a single point in the line.
Analytical solutions of both traveling waves or bound states are obtained,
which provide valuable insight into the dynamics of CTQW. The number of bound
states is found to be critically dependent on the defect parameters, and the
localized probability peaks can be readily obtained by projecting the CTQW
wavefunction on to these bound states. The interference between two bound
states are also observed in the case of a transition defect. The spreading of
CTQW probability over the line can be finely tuned by varying the position and
transition defect parameters, offering the possibility of precision quantum
control of the system.
