Plot the function f(alpha a) = 5 sin(alpha a)/alpha a + cos alpha a for 0 lessth
ID: 2085929 • Letter: P
Question
Plot the function f(alpha a) = 5 sin(alpha a)/alpha a + cos alpha a for 0 lessthanorequalto alpha a lessthanorequalto 4 pi. This is the left-hand side of the transcendental equation that we have to solve to find the allowed energies of an electron in the Kronig-Penney potential. (a) Now, given the right-hand side of the transcendental equation, f(alpha a) = cos ka, what are the allowed values of alpha a? (b) What are the specific values of alpha a at ka = pi and ka = 2 pi? Working from your plot from the problem above and assuming a = 0.42 nm, find the energetic width (in eV) of the allowed energy band for 0Explanation / Answer
Matlab code:
clc
clear all
close all
aa = 0:1/10:4*pi;
f_aa = (5*sin(aa))./aa + cos(aa);
plot(aa,f_aa)
grid on
xlim([0 4*pi])
syms aa
%ka = pi;
eqn = (5*sin(aa))./aa + cos(aa) == cos(pi);
solx1 = solve(eqn, aa)
syms aa
%ka = 2*pi;
eqn = (5*sin(aa))./aa + cos(aa) == cos(2*pi);
solx2 = solve(eqn, aa)