Part IV: Three-Dimensional Systems
Moving to three dimensions: central potentials, orbital angular momentum, spherical harmonics, and the hydrogen atom—one of the most important exactly solvable systems in quantum mechanics.
70+ pages | 7 chapters
1. 3D Schrödinger Equation (7 pages)
Laplacian in 3D, separation of variables, spherical coordinates
2. Central Potential (9 pages)
Radial equation, effective potential, boundary conditions
3. Orbital Angular Momentum (12 pages)
Angular momentum operators, commutation relations, eigenvalues
4. Spherical Harmonics (10 pages)
Y_lm(θ,φ), orthonormality, addition theorem
5. Hydrogen Atom (15 pages)
Coulomb potential, Laguerre polynomials, quantum numbers, fine structure
6. 3D Harmonic Oscillator (8 pages)
Isotropic oscillator, degeneracy, Cartesian vs spherical
7. 3D Scattering Theory (9 pages)
Partial waves, phase shifts, optical theorem