7_tight_binding_model_sol.md

import matplotlib
from matplotlib import pyplot

import numpy as np

from common import draw_classic_axes, configure_plotting

configure_plotting()

pi = np.pi

Solutions for lecture 7 exercises

Exercise 1: Lattice vibrations

Subquestion 1

Hint: Normal modes have the same function as \mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3 have in \mathbb{R}^3. That is, for every vector \mathbf{v} we have \mathbf{v} = a\mathbf{e}_1 + b\mathbf{e}_2 + c\mathbf{e}_3.

Hint: The lecture concerns atom vibrations, so what will a phonon be?

??? hint "Major hint"

What's the question's title?

Hint: What kind of particles obey Bose-Einstein statistics? What kind of 'particles' are phonons?

Subquestion 2