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hschia
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In quantum mechanics, what is the difference between velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
Wikipedia said:The variable v can either be taken to be the speed of the particle or the group velocity of the corresponding matter wave.
v = vg = [itex]\frac{\partial \omega}{\partial k}[/itex], that is, group velocity equals the velocity of the particle associated with the wave or wave packet.hschia said:My essential question is, what is the difference between vp and v here? Isn't vp=ω/κ, the same idea as the ''PURE'' velocity of wave?
Velocity refers to the rate of change of position over time, while phase velocity refers to the rate of change of phase over time. In matter waves, velocity is related to the physical movement of the wave, while phase velocity is related to the oscillation of the wave.
The velocity of matter waves is determined by the de Broglie wavelength, which is calculated by dividing Planck's constant by the momentum of the particle. This wavelength is then used to calculate the velocity of the wave using the wave equation.
The velocity of matter waves can be affected by the mass and energy of the particle, as well as external factors such as electric and magnetic fields. The medium through which the wave is traveling can also impact its velocity.
No, the phase velocity of matter waves cannot exceed the speed of light. This is because matter waves are bound by the laws of special relativity, which states that nothing can travel faster than the speed of light.
The group velocity of a matter wave is the velocity at which the overall amplitude of the wave propagates, while the phase velocity is the velocity at which the individual wave peaks move. In most cases, the group velocity is equal to the phase velocity, but there are certain situations where they can differ.