num.m

function Triangle_well()
clear all, clc;                          
%https://ru.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%86
h  = 1;             
e  = 1;             
m  = 1;             
EH = 4.3597441775*10^-18; %Хартри 
E  = 100000 / (5.1422065211.*10.^11);

warning('off', 'MATLAB:integral:NonFiniteValue');
w      = @(x, a) x.*exp(-a.*x);
w_     = @(x, a) exp(-a.*x) - a.*x.*exp(-a.*x);
U      = @(x) e.*E.*x; 

No     = @(a) integral(@(x) w(x,a).^2, 0, inf); %normalization
J1     = @(a) h^2/(2*m) * integral(@(x) w_(x, a).^2, 0, inf);
J2     = @(a) integral(@(x) U(x) .* w(x, a).^2, 0, inf);
J      = @(a) J1(a) + J2(a);
E_F    = @(a) J(a)/No(a);%total evergy
E_F_SI = @(a) E_F(a)/ EH; %total evergy
amin = 0;
amax = 0.04;
a0   = fminbnd(E_F, amin, amax);
display(a0);
display(E_F_SI(a0));
hold on;
fplot(E_F, [amin amax]);
axis([amin, amax, 0, 0.001])

end