Wave packet description of electrons in solid state physics

In summary, the velocity of a bloch electron in solid state physics is given by ##\frac{\partial E(k)}{\partial k}##, derived from the assumption that electrons are wave packets in bloch states in solids. However, there is concern about the formula's ability to describe long-term evolution of electron states, as wave packets break down over time. The velocity is for a very broad wave packet, but an infinitely broad wave packet cannot disperse any further.
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taishizhiqiu
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In solid state physics, I learned that the velocity of a bloch electron is ##\frac{\partial E(k)}{\partial k}##, where ##E(k)## is the energy dispersion. This formula is derived on the basis of the assumption that electrons is a wave packet of bloch state in solids.

However, I have a question concerning this statement:

I learned solid state physics three years ago and I am now a Ph.D. student. However, I still cannot convince me of the original statement because I know a wave packet BREAKS DOWN with time evolution. I can't imagine this formula can describe long time evolution of electron states.

Can anyone give me some confidence of this formula?
 
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This is the velocity for a very broad wavepacket (in real space), i.e. a very localized state in k-space. (If not, for which k-state would you have to take the derivative?) But an infinitely broad wavepacket can't disperse any further.
 
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FAQ: Wave packet description of electrons in solid state physics

1. What is a wave packet in solid state physics?

A wave packet in solid state physics is a mathematical description of the behavior of electrons in a solid material. It represents the probability of finding an electron at a particular position with a particular energy.

2. How is the wave packet description used in solid state physics?

The wave packet description is used to understand the behavior of electrons in solid materials, such as in semiconductors, metals, and insulators. It helps to explain phenomena such as conductivity, band structure, and energy levels.

3. How is a wave packet different from a classical particle?

A wave packet is different from a classical particle in that it takes into account the wave-like nature of electrons. Unlike a classical particle, which has a definite position and momentum, a wave packet represents a range of positions and momenta that an electron can occupy.

4. What factors affect the shape and size of a wave packet?

The shape and size of a wave packet are affected by several factors, including the energy and momentum of the electron, the potential energy of the material, and the temperature. Additionally, the shape and size may change as the electron moves through the material.

5. Can the wave packet description be applied to other particles besides electrons?

Yes, the wave packet description can be applied to other particles, such as photons and other elementary particles. It is a useful tool for understanding the behavior of quantum particles in various systems, including solid state materials.

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