  We studied two possible approaches to one-dimensional Levinson's theorem for
Sch\"odinger equation. The first one, we restrict the 3-dimensional theorem.
The other one, the theorem proposed by Dong, Ma and Klauss \cite{Dong}. We find
failures in each approach for a one-dimensional reflectionless potential. In
order to see this, we explicitly evaluate the phase shift using Schr\"odinger
equation using solution procedure proposed by Jaffe \cite{Jaffe}.
