a=5.51e-10;
m=9.11e-31;
Emax=100*(1.6e-19);
H=1.055e-34;
p=10;
alpha=linspace(0,205,100000);
E=linspace(0,Emax,100000);
alpha=sqrt(2*m*E)/H;
LHS=cos(alpha*a) + p*sin(alpha*a)./(alpha*a);
plot(alpha,LHS,-alpha,LHS);
ylabel('LHS');
xlabel('alpha');

E=linspace(0,Emax,100000);
b=sqrt(2*m)*(a/H);
k=(acos((10*sin(b*sqrt(E))./(b*sqrt(E))+cos(b*sqrt(E)))))./(a);
plot(k,E,-k,E);
grid on;
xlabel('k');
ylabel('E');

E=linspace(0,2.5e-19,1000);
b=sqrt(2*m)*(a/H);
k=(acos((10*sin(b*sqrt(E))./(b*sqrt(E))+cos(b*sqrt(E)))))./(a);
plot(k,E,-k,E);
grid on;
xlabel('k');
ylabel('E');