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World 5 · Reciprocal space and Brillouin zones · 8 min · PRO

Equivalent Bloch wavevectors

PRO · Crystal Lab

World 5: Reciprocal space and Brillouin zones is part of PRO

The first world of Crystal Lab is free. PRO opens the other 24 lessons in 8 worlds — simulations, quizzes and all.

  • A cell in wavevector space
  • Large cells, small reciprocal scales
  • A gap from alternating hopping
  • Bands repeat beyond a zone
  • Rotate a crystal, move its reflections
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  • Practice exams and certificates

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← Large cells, small reciprocal scalesA gap from alternating hopping →

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