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...
icon
Related questions
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.
Transcribed Image Text: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.
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Absorption and Adsorption
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY