  We propose an exact method for solving a one-dimensional Schr\"odinger
equation. An arbitrary potential is represented by the collection of
short-width potentials. For building the collection scheme, a new solvable
potential is introduced. It is based on the simple expansion of the
wavefunction of the introduced potential. The illustration of the scheme is
done by reproducing the results of the rectangular potential. The scheme has
computational advantages and the transmission properties, eigenenergies can be
calculated efficiently. The presented scheme is compared with the other similar
schemes in terms of computational complexity, analytical solubility, etc.. A
\textit{Mathematica} code is provided in the supplementary file that solves the
Schr\"odinger equation with arbitrary potential function $V(x)$ and effective
mass $m(x)$.

Quantum Physics