Why Use Reciprocal Lattice for Band Structure?

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SUMMARY

The discussion centers on the importance of the reciprocal lattice in band structure calculations. It highlights that most lattices exhibit translation invariance, making momentum a conserved quantum number. This conservation allows for a diagonal representation of conserved quantities in momentum space, simplifying calculations significantly. Understanding this relationship is crucial for analyzing band structures effectively.

PREREQUISITES
  • Basic knowledge of quantum mechanics and solid-state physics
  • Understanding of band structure and dispersion curves
  • Familiarity with lattice structures and their properties
  • Concept of momentum as a quantum number
NEXT STEPS
  • Study the principles of reciprocal lattice in solid-state physics
  • Learn about the calculation methods for band structure using software like VASP or Quantum ESPRESSO
  • Explore the implications of momentum conservation in quantum mechanics
  • Investigate the relationship between lattice symmetry and band structure
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Physicists, materials scientists, and students studying solid-state physics who are interested in understanding band structure and its calculations.

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Reciprocal lattice?

Hi everybody...
I'm read about the band structure and the dispersion curve,I've got informations about the reciprocal lattice and how we determine it, but what I want to know why we use the reciprocal lattice in band structure calculations?

thanks
 
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because most lattices are translation invariant, momentum is a "good" quantum number, i.e. it is conserved. this leads to a diagonal representation of all other conserved quantities in the momentum space, which is especially simple to work with.
 

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