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Wave Mechanics

Waves are one of the most fundamental phenomena in physics—they are present in everything. From our everyday experience, we interact with sound waves and light (electromagnetic waves). Much of our technology is also based on waves—the internet, for example, relies on electromagnetic waves to transmit data. Springs in cars and buildings are designed to absorb mechanical waves, while radio waves are used for communication. More fundamentally, quantum mechanics posits that waves are the underlying nature of all particles.

It might be surprising to see that one idea—the wave—can be used to describe so many different phenomena. As such, it is important to understand what these phenomena have in common. Fundamentally, they are a result of:

  1. Time-translational invariance: The laws of physics do not change over time.
  2. Locality: Causation only occurs in the immediate vicinity of an event.
  3. Linearity: The superposition principle holds, meaning that the sum of two solutions is also a solution.

These three principles are the foundation of wave mechanics, and they will be the focus of this chapter.