Introduction to Quantum Mechanics · Problem 5.28

Identical Particles — David J. Griffiths

Physics — Quantum Mechanics · band_structure_plot

Problem

Make a plot of

E

vs.

q

for the band structure in Section 5.3.2. Use

\alpha = 1

(in units where

m = \hbar = a = 1

). Hint: In Mathematica, ContourPlot will graph

E(q)

as defined implicitly by Equation 5.71. On other platforms the plot can be obtained as follows: • Choose a large number (say 30,000) of equally-spaced values for the energy in the range

E = 0

and

E = 30

. • For each value of

E

, compute the right-hand side of Equation 5.71. If the result is between

-1

and 1, solve for

q

from Equation 5.71 and record the pair of values

\{q, E\}

and

\{-q, E\}

(there are two solutions for each energy). You will then have a list of pairs

\{\{q_1, E_1\}, \{q_2, E_2\}, \ldots\}

which you can plot.

Related theory

Vibration Rotation Coupling And Band Structure

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