Understanding of crystal wave vector

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SUMMARY

The discussion centers on the distinction between electron wave vectors and crystal wave vectors in the context of solid-state physics. The crystal wave vector is not merely a vector sum of individual electron wave vectors; rather, it represents the collective behavior of electrons in a crystal lattice. The crystal wave vector is associated with group velocity, while the individual electron wave vector pertains to phase velocity. Understanding the relationship between group velocity, defined as 'delta_omega/delta_k', is crucial for interpreting wave propagation in crystals.

PREREQUISITES
  • Schrödinger wave equation fundamentals
  • Concept of wave functions in quantum mechanics
  • Understanding of group velocity and phase velocity
  • Basic principles of solid-state physics and crystal lattices
NEXT STEPS
  • Study the relationship between group velocity and crystal wave vectors in solid-state physics
  • Explore the implications of density of states in electron behavior
  • Learn about the mathematical derivation of 'delta_omega/delta_k'
  • Investigate the role of wave vectors in band theory of solids
USEFUL FOR

Students and professionals in physics, particularly those focused on solid-state physics, quantum mechanics, and materials science, will benefit from this discussion.

Urmi Roy
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Hi All,

From the Schrödinger wave equation, I kind of understand what a wave function and hence a wave vector is, so I understand what a wave vector of an electron wave is.
However while talking about crystals, there is also a 'crystal wave vector'. Is this a vector sum of wave vectors of individual electrons?
While finding density of states of electrons, why is the electron wave vector used instead of the crystal wave vector?
 
So I've read that crystal wave vector corresponds to the group velocity while the electron's individual wave vector corresponds to it's phase velocity. However I'm still not sure if that means that the crystal wave vector means that it's effectively a 'net' or a sum of the individual ones.

The basic problem is that the group velocity is defined as 'delta_omega/delta_k', so what does this mean intuitively?
 

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