Quantum mechanics waves : part 1

In classical physics, waves are described as periodic disturbances or oscillations that transfer energy through a medium or space without the physical transport of matter. The medium can be solid, liquid, or gas, depending on the type of wave.
Key characteristics of classical waves include:
1. Wave Types:
• Mechanical Waves: Require a medium to propagate (e.g., sound waves, water waves).
• Transverse Waves: The particles of the medium oscillate perpendicular to the direction of wave propagation (e.g., water waves, electromagnetic waves).
• Longitudinal Waves: The particles of the medium oscillate parallel to the direction of wave propagation (e.g., sound waves).
• Electromagnetic Waves: Do not require a medium and can propagate through a vacuum (e.g., light waves, radio waves).
2. Wave Properties:
• Wavelength (): The distance between two consecutive crests or troughs in a wave.
• Frequency (): The number of oscillations or cycles per unit time, measured in Hertz (Hz).
• Period (): The time taken for one complete oscillation ().
• Amplitude (): The maximum displacement of the wave from its equilibrium position, which determines the wave’s energy.
• Wave Speed (): The speed at which the wave propagates, given by .
3. Wave Behavior:
• Reflection: Waves bounce back upon encountering a boundary.
• Refraction: Waves change direction and speed when transitioning between different media.
• Diffraction: Waves bend around obstacles or spread out after passing through small openings.
• Interference: Waves superimpose to form constructive (amplitude increases) or destructive (amplitude decreases) interference patterns.
4. Mathematical Representation:
• A wave is often described by a wave equation:

Where:
• : Amplitude
• : Wave number
• : Angular frequency
• : Phase constant
• : Position
• : Time
5. Energy Transfer:
• Waves carry energy through oscillations. For mechanical waves, the energy depends on the medium’s elasticity and density, while for electromagnetic waves, it depends on the electric and magnetic fields’ interaction.
Classical wave theory provides the foundation for understanding natural phenomena such as sound, light, water waves, and seismic waves.