The one-dimensional hydrogen atom has been at the center of controversies and debate ever since Loudon (1952) published his theoretical work on the system. Since then, it has been debated if the system has an infinite or a finite energy ground state, whether there are energy degeneracies, violating the one-D non-degeneracy theorem, whether the states are localized (symmetry broken) on either side of the singularity (x = 0) or delocalized across the origin, and are parity eigenstates as well. There is no unequivocal or concrete experimental evidence on the existence of the hydrogen atom in one dimension and its spectral signatures; but there have been several attempts to define limiting experimental conditions (e.g., high magnetic field) which may lead to the realization of the one-dimensional H-atom and recording of its spectrum. Calculations of Landau & Lipshitz, which dealt with giving an estimate of the strength of such magnetic field, emphasize that the highest available magnetic fields in the laboratory is almost negligible compared to the range of the magnetic field strength required to approach the condition for the realization of the one-D H-atom. Some experiments on quasi-one-D polymer chains, which resembles the system of the one-D H-atom, reported optical absorption spectra with the dominance of the ground state. There are other such examples, such as semiconductor quantum wires and carbon nanotubes, , which reported various forms of the absorption spectra. However, these results are inadequate to characterize the exact experimental form of the absorption spectrum of one-D H-atom, as the conditions for its realization are still elusive. Thus, the one-D H-atom has largely remained a theoretical problem to test various theoretical techniques of handling quantum mechanical problems of the present kind. The result of all these investigations do not seem to have converged to a generally accepted conclusion about the nature of quantum states supported by the 1-D Coulomb potential, or their number. More significantly, the spectral signature of the 1-D H-atom, if it exists, is not yet known. Among the theoretical investigations, the series expansion method, Fourier transform method, Supersymmetric method and insertion of cut-off potential to the one-D potential function method , infinite number of discrete quantum states with exactly the same energy levels as found in the 3-D hydrogen atom, the reduction in the dimension (from 3 to 1) notwithstanding. However, these results are confined to research journals and reviews and are not easily accessible or comprehensible to chemists or students of chemistry, who could ultimately play a crucial role in the eventual experimental realization of the 1-D H-atom, if it exists. It is primarily this objective, that has guided us in exploring the problem and writing this article.