Quantum mechanics || Matter wave || Group velocity || Phase velocity

Описание: This video from Physics Practical provides an introduction to quantum mechanics, specifically focusing on matter waves and their properties. Here is a summary of the key concepts covered:

Introduction to Matter Waves (0:05 - 2:05)
The concept that a moving particle is associated with a wave was introduced by De Broglie.
This phenomenon is known as the matter wave or De Broglie wave.

De Broglie Wavelength Formulas (2:20 - 12:43)
The formula for the wavelength of a matter wave is λ = h/p, where h is Planck's constant and p is the momentum of the particle (2:44).
Momentum can be expanded to p = mv (mass × velocity), making the formula λ = h/mv (3:11).
The video derives these formulas using Einstein's mass-energy relation (E=mc²) and photon energy (E=hν) (3:50-5:30).
Additional expressions for the wavelength are provided in terms of kinetic energy (λ = h/√(2mE)) (9:44) and temperature (λ = h/√(3mkBT)) (11:13).

Properties of Matter Waves (13:40 - 26:38)
Velocity Dependency: Wavelength is inversely proportional to velocity and mass (13:53). A faster particle has a shorter wavelength.
Rest Particle: If a particle is at rest (v=0), its wavelength becomes infinite (16:08), implying matter waves only exist for particles in motion.
Wave Velocity vs. Light Velocity: The velocity of matter waves is generally greater than the velocity of light (25:51). The velocity of a matter wave is not constant, unlike the constant speed of electromagnetic waves (18:20).

Phase Velocity (28:33 - 37:20)
The video defines phase velocity (or wave velocity) as the speed at which the wave advances through a medium (29:32).
It is mathematically defined as the ratio of angular frequency to the wave propagation constant (vp = ω/k) (31:01).#physics​
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