2.5 a) Calculate the five lowest "free electron" bands along the 4-axis in the Brillouin zone for the simple cubic lattice (analogous to Fig. 2.35). Calculate the associated eigenfunctions. b) For bands which are degenerate along the 4-axis (or at I or at X), construct linear combinations of the wave functions in such a way that the new func-

2.5 a) Calculate the five lowest "free electron" bands along the 4-axis in the Brillouin zone for the simple cubic lattice (analogous to Fig. 2.35). Calculate the associated eigenfunctions. b) For bands which are degenerate along the 4-axis (or at I or at X), construct linear combinations of the wave functions in such a way that the new func-

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

2.5
a) Calculate the five lowest "free electron" bands along the A-axis in the
Brillouin zone for the simple cubic lattice (analogous to Fig. 2.35). Calculate
the associated eigenfunctions.
b) For bands which are degenerate along the 4-axis (or at r or at X), construct
linear combinations of the wave functions in such a way that the new func-
464
Problems to Chapters 1-9
tions are either invariant to the group operations, or reduce to sets of
functions which transform into one another. Such sets form the basis func-
tions for the irreducible representations of the group of the k-vector.

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