The first real clue to the nature of atoms was the discovery of characteristic atomic spectra, which suggested that atoms have discrete energy levels, and can create and emit real photons that carry off the energy difference between two levels.

Quantum description of hydrogen, 1 proton and 1 electron, in terms of standing waves of probability for the one electron! The two quantum numbers are the principal quantum number n and the “angular momentum” quantum number ℓ, represented by letters s (0), p (1), d (2), etc.

The space quantum numbers are n, ℓ and m. It's important to understand that the “angular momentum” quantum number ℓ has nothing to do with classical angular momentum. Rather, it is related to the form of the three-dimensional standing probability wave for that state. The values of ℓ and m determine the specific form of a ubiquitous function known as Ym(θ, φ), aka “spherical harmonics,” in spherical polar coordinates.
To understand more, we need to learn about spin, an intrinsic or internal quantum number for all fundamental particles, and the Pauli Principle!