QM1 · One-dimensional problems
A 26-module path through qm1 · one-dimensional problems, in study order from foundations to the frontier.
Modules
- Time-Independent Schrödinger Equation in One Dimension
- Bound States versus Scattering States
- Infinite Square Well
- Finite Square Well
- Free Particle and Plane Waves
- Wave Packets and Their Construction
- Group Velocity versus Phase Velocity
- Wave Packet Spreading and Dispersion
- Quantum Harmonic Oscillator: Analytic Solution
- Ladder Operators and the Algebraic Oscillator
- Hermite Polynomials and Oscillator Eigenfunctions
- Zero-Point Energy
- Delta-Function Potential Well and Bound State
- Delta-Function Barrier and Scattering
- Matching Conditions and Wavefunction Continuity
- Potential Step and Reflection
- Rectangular Barrier and Quantum Tunnelling
- Transmission and Reflection Coefficients
- Probability Current in One Dimension
- Resonant Transmission and Tunnelling Resonances
- Bohr–Sommerfeld and Semiclassical Quantization in 1D
- Parity Symmetry of One-Dimensional Eigenstates
- Node Theorem and Energy Ordering
- Coherent States of the Harmonic Oscillator
- Non-Degeneracy of One-Dimensional Bound States
- The Particle in a Three-Dimensional Box