QM5 · Central potentials & hydrogen
A 20-module path through qm5 · central potentials & hydrogen, in study order from foundations to the frontier.
Modules
- Separation of Variables in Spherical Coordinates
- The Radial Equation
- Effective Potential and the Centrifugal Barrier
- Boundary Conditions and Normalization of Radial Wavefunctions
- Degeneracy and the Role of the Magnetic Quantum Number
- The Hydrogen Atom: Coulomb Radial Equation
- The Bohr Energy Spectrum and Rydberg Constant
- Hydrogenic Wavefunctions and Quantum Numbers
- Radial Probability Distribution and Expectation Values
- The Bohr Radius and Characteristic Atomic Scales
- Accidental Degeneracy and the SO(4) Symmetry
- The Laplace–Runge–Lenz Vector in Quantum Mechanics
- Hydrogenic Ions and Scaling with Nuclear Charge
- The Three-Dimensional Isotropic Harmonic Oscillator
- Degeneracy and SU(3) Symmetry of the 3D Oscillator
- The Free Particle in Three Dimensions
- Spherical Bessel and Neumann Functions
- Spherical Hankel Functions and Outgoing Waves
- Particle in a Spherical Well and Infinite Spherical Box
- Partial Wave Expansion of Plane Waves