In undergraduate courses of Chemistry, quantum mechanics of one-dimensional systems occupy a prominent position. Quantum states of a particle in a one-dimensional potential well, rigid rotator on a plane, harmonic oscillator, etc. are taught to demonstrate the techniques of arriving at solutions of the Schrodinger equation (SE) posed as a boundary value problem, emphasizing at the same time the importance of all mathematical conditions imposed on the wavefunctions. It is almost mandatory in all such courses to venture a little beyond and discuss quantum mechanics of the hydrogen atom in three dimensions. The bound energy levels and wave functions of the hydrogen atom are key to the development of general ideas and understanding of the level structures of heavier atoms. The (SE) for H-atom in 3D is not separable in Cartesian system of coordinates. The standard textbook recipe has been to transform the energy eigenvalue equation from Cartesian (x, y, z) to spherical polar coordinates (r, θ, ϕ) and separate the angular and the radial parts Rnl(r) of the wave equation which are then analytically solved. The former turns out to be the spherical harmonics [Y l m (θ, ϕ)] while the latter takes the form of the associated Laguerre polynomials. The total wave function inversion symmetric. Its signature, the parity, is a 'good' quantum number and the hydrogenic levels alternately belong to even and odd parity. We note, however, that V (r ⃗) is singular at the origin (|r| ⃗⃗⃗⃗⃗ = 0). The role of the singularity, if any, in shaping the radial wavefunctions is usually bypassed or underemphasized at the introductory level of the undergraduate courses in Chemistry. But several issues do come up and require careful handling while discussing the behavior of Ψ, in the neighborhood of |r ⃗| = 0. Whatever be the 'parity', the allowed quantum states have (2l + 1) fold degeneracy (the m-degeneracy, the magnetic quantum number 'm' taking integer values from -l to l in steps of 1) arising from the rotational symmetry of the hydrogen atom. There is also an extra l-degeneracy (e.g., 2s, 2p) not connected with the rotational symmetry. It has been often called an accidental degeneracy, the origin of which is a dynamical symmetry. The hydrogenic energy levels turn out to be dependent only on the principal quantum number ( Enlm = -R n 2 , n = 1, 2, 3,...) revealing the l and m degeneracies referred to.