Unit: Classical waves in non-dispersive systems: ropes and coaxial transmission lines

This unit illustrates standing and traveling waves in the context of classical mechanics (waves in a rope) and classical electromagnetism (charge and voltage oscillations in a coaxial cable). The idea of a dispersion relation is introduced. Propagation, reflection and transmission at an abrupt boundary, superposition, attenuation, and energy are explored.

Basic concepts (50 minutes)

Traveling and standing waves: Non-dispersive wave equation & initial conditions (60 minutes)

Standing waves: Physics and the measurement of a dispersion relation (xx minutes)

Reflection, transmission and impedance (xx minutes)

Energy (50 minutes)

Superposition & Fourier analysis (xx minutes)

Unit: Quantum waves: The Schrödinger equation

This unit examines quantum systems in the context of the Schrödinger equation, which is an example of a dispersive wave equation. We discuss mostly bound states, but also unbound states. The students draw on their knowledge of quantum systems from the Spins paradigm, and extend it to the case of a continuum of observables (position), which allows a discussion of probability density and the probability of locating a particle in a particular region of space. The other lessons from the quantum postulates encountered in the Spins paradigm (measurement, superposition, time evolution etc.) are re-examined in this new language.

The wave function (xx minutes)

The finite (square) potential energy well (xx minutes)

The infinite well & superposition, measurement, probability etc. (xx minutes)

Time Evolution (xx minutes)

Unbound states, barriers & tunneling (xx minutes)

Heisenberg Uncertainty Principle & time evolution of a Gaussian wave packet (xx minutes)

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