%constants
h2=1.05e-34;
mass=9.11e-31;
a=5.51e-10;
p=11;
Emax=100*1.6e-19;
%Figure(4) using the K in the last question
E=linspace(0,3e-19,1000);
alpha=sqrt(2*mass*E)/h2;
LHS=((p/a)*sin(alpha*a)./alpha)+cos(alpha*a);
k=acos(LHS)./a;
%first derivative
dy=diff(E)./diff(k);
dy=[min(dy),dy];
%second derivative
dyy=diff(dy)./diff(k);
dyy=[max(dyy),dyy];
%effective mass
eff_mass=(h2^2)./dyy;
%plotting two curve the positive and the negative
plot(k,eff_mass,-k,eff_mass);

 %part 2
 %taking the equation from the user
sc = inputdlg('Type an expression that is a function of ‘k’:' );    % Cell Output
k1= sc{:};                                                          % Function String
k_fun= str2func(['@(k)' k1])  ;                                      % Not Vectorized (Illustration Only)
 k_funv= str2func(['@(k)' vectorize(k1)]);
 %first derivative
 first=diff(k_funv(k))./diff(k);
 first=[max(first),first];
 %second derivative
 second=diff(first)./diff(k);
 second=[min(second),second];
 %effective mass
 eff_mass2=(h2^2)./second;
 plot(k,eff_mass2,(-1)*k,eff_mass2);