Group velocity of wavepacket

In summary, the conversation discusses the use of the group velocity equation, vgroup(k) = ∇kEk, in finding the group velocity of a wavepacket in an inhomogeneous lattice. The question is raised about the use of a homogeneous dispersion in this calculation. The expert explains that the formula applies to any dispersion relation and the group velocity represents the overall shape of the wave, regardless of the system. The importance lies in the difference between calculating it in a homogeneous and inhomogeneous system.
  • #1
Niles
1,866
0
Hi

The group velocity of an electron wavepacket in a homogeneous lattice is

vgroup(k) = ∇kEk,

where Ek is the dispersion. I have just read an article, where they use this to find the group velocity of a wavepacket in an inhomogeneous lattice, but they use the homogeneous dispersion. I don't quite understand why this is allowed. Can you clarify this?


Niles.
 
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  • #2
would u clarify what you mean by homogeneous dispersion? what is an inhomogeneous lattice?
 
  • #3
I mean homogeneous when there is no impurity. Likewise I mean inhomogeneous when there is an impurity.
 
  • #4
icic... I am not sure if I understand your question. But your given formula is actually the definition of the group velocity, and it applies to any dispersion relation. This group velocity means the velocity of the overall shape of the wave and it doesn't matter what your system is.

I guess what matters, probably in your problem, is how different it would be when you calculate it in homogeneous and inhomogeneous system.
 

Related to Group velocity of wavepacket

What is group velocity?

Group velocity is a measure of how fast the overall shape or envelope of a wavepacket moves through a medium. It is the speed at which information is transmitted by a wave.

What factors affect the group velocity of a wavepacket?

The group velocity of a wavepacket is affected by the properties of the medium it is traveling through, such as its density and stiffness. It is also influenced by the frequency and wavelength of the wave, as well as any external forces or interactions.

How is group velocity different from phase velocity?

Group velocity and phase velocity are related but distinct concepts. Phase velocity is the speed at which the individual wave cycles are moving, while group velocity is the speed at which the entire wavepacket is moving. In some cases, these velocities may be different, especially when the wavepacket is dispersed.

What is the significance of the group velocity in wave mechanics?

The group velocity is an important concept in wave mechanics because it helps us understand how waves behave and interact with their surrounding medium. It also has practical applications, such as in the design of communication systems and understanding the behavior of light in optical fibers.

How is the group velocity of a wavepacket measured?

The group velocity of a wavepacket can be measured experimentally by tracking the movement of the wave's envelope. It can also be calculated using mathematical equations that take into account the properties of the medium and the wave's frequency and wavelength.

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