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For the direct problem, we give the asymptotic distribution of the (real and nonreal) transmission eigenvalues for the Schrödinger 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 nonzero value related to the potential (whereas without the certain constant  γ ). The reconstruction algorithms are also revealed.

On the direct and inverse transmission eigenvalue problems for the Schrödinger operator on the half line