  We present exact energy spectrum and eigenfunctions of the one-dimensional
hydrogen atom in the presence of the minimal length uncertainty. By requiring
the self-adjointness property of the Hamiltonian, we completely determine the
quantization condition. We indicate that the single-valuedness criteria of the
eigenfunctions in non-deformed case is an emergent condition and the
semiclassical solutions exactly coincide with the quantum mechanical results.
The behavior of the wave functions at the origin in coordinate space and in
quasiposition space is discussed finally.
