  For the direct problem, we give the asymptotic distribution of the (real and
non-real) transmission eigenvalues for the Schrodinger operator on the half
line. For the inverse problem, we prove that the potential can be uniquely
determined by all transmission eigenvalues, the parameter in the boundary
condition and some non-zero value related to the potential (whereas without the
certain constant {\gamma}). The reconstruction algorithms are also revealed.
