Part III: One-Dimensional Systems
Exact solutions to the Schrödinger equation in one dimension. We study the free particle, square wells, the harmonic oscillator, and tunneling phenomena—building physical intuition for quantum behavior.
Part Overview
One-dimensional systems are exactly solvable and provide crucial insights into quantum phenomena: bound states, energy quantization, tunneling, and the role of boundary conditions.
55+ pages | 7 chapters
Chapters
1. Free Particle (7 pages)
Plane waves, wave packets, group velocity, dispersion
2. Infinite Square Well (8 pages)
Energy quantization, wavefunctions, orthonormality
3. Finite Square Well (9 pages)
Bound states, exponential tails, transcendental equations
4. Quantum Harmonic Oscillator (12 pages)
Ladder operators, Hermite polynomials, coherent states
5. Delta Function Potential (6 pages)
Bound state, scattering states, transmission and reflection
6. Scattering & Tunneling (8 pages)
Barrier penetration, tunnel effect, resonant tunneling
7. WKB Approximation (5 pages)
Semi-classical methods, connection formulas, tunneling rate