One-Electron Atoms

Phase 1: The Foundation

Syllabus Goal

Understand basic quantum mechanics of atoms. Master energy levels and quantum numbers of hydrogenic atoms.

Schrödinger Equation for Hydrogen

Radial and Angular parts separation: $$ \Psi_{n\ell m}(r, \theta, \phi) = R_{n\ell}(r) Y_{\ell m}(\theta, \phi) $$

Quantum Numbers

1. Principal ($n$): Energy level ($E_n \propto -1/n^2$).
2. Azimuthal ($\ell$): Orbital angular momentum ($0 \le \ell < n$).
3. Magnetic ($m_\ell$): Projection of $L$ ($-\ell \le m_\ell \le \ell$).

Energy Levels

Degeneracy of level $n$ is $n^2$ (ignoring spin).