The one-dimensional hydrogen atom has been a controversial problem with a fairly long history, but its importance in understanding how the calculus of quantum mechanics operates in singular potentials, can hardly be overestimated. In this article, we briefly trace the history of hydrogen atom in one dimension and elucidate how the standard Frobenius method (a generalized series expansion method) can be applied to this system vitiated as it is, by the singularity at the origin. As expected, the conditions that the wave function 𝛹(𝑥) must be single valued and continuous with continuous first derivative, 𝛹 remaining finite everywhere (including the singular point) and vanishing at the outer boundaries' (𝑥 = ±∞) play a key role in shaping the energy eigenfunctions and the corresponding energy eigenvalues.