Welcome to the hydrogen atom: the hydrogen of atoms. The starter pack of quantum mechanics. The MVP of Schrödinger’s early access demo. 🧠 Why do we care about hydrogen? Because it’s the only atom we can solve exactly using the Schrödinger equation. It’s just: One electron One proton One huge existential crisis 📜 Schrödinger says: We solve the time-independent Schrödinger equation in spherical coordinates: $$ -\frac{\hbar^2}{2\mu} \nabla^2 \psi(r, \theta, \phi) - \frac{e^2}{4\pi \varepsilon_0 r} \psi = E \psi $$ ...