The Hydrogen Atom
PHYS 410 · Module 5
This module studies the quantum mechanics of hydrogen, the most important exactly solvable atom. Students learn separation of variables, angular momentum, spherical harmonics, energy levels, orbitals, and selection rules.
Lessons in this module
Central force problems and separation of variables
The hydrogen atom is governed by a central Coulomb potential. This lesson explains spherical coordinates, separation of variables, radial and angular equations, and quantum numbers.
Angular momentum and spherical harmonics
Angular momentum in quantum mechanics is quantized and described by operators. This lesson explains $L^2$, $L_z$, magnetic quantum numbers, and spherical harmonics.
Hydrogen energy levels and wavefunctions
Hydrogen's bound-state energies depend primarily on the principal quantum number. This lesson explains the Bohr energy formula, degeneracy, radial probability, and orbital interpretation.
Selection rules and spectra
Atomic spectra arise from transitions between quantized energy levels. This lesson explains photon emission and absorption, dipole selection rules, and the structure of hydrogen spectral lines.
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