Abstract: The potential energy for one- dimensional hydrogen atom is usually modelled by- 1 / ｜ x ｜ over the entire space x∈（- ∞,∞）. Studies over years reach a consensus that the space is separated into two impermeably semi- infinite spaces due to the serious singularity of the potential. In the two spaces,there exist two independent one- dimensional hydrogen atoms.

Key words: one-dimensional hydrogen atom, space-splitting, singular potential