yoba.m

m_e = 9.10938356 * 10 .^-31;
E = 10;
alpha = 1;
from = 0;
to = 1000;
v0 = 0.5 .* 299792458;
p =  m_e * v0;

w = @(x) { x .* exp(-alpha .* x) };
N2 = @(x) { integral(w, from, to) };
U = @(x) { 10 .* x };

Ham = @(x) { p .^ 2 / 2 .* m_e + U(x)};
J = @(x) { integral(@(x) { w(x) .* Ham(x) .* w(x) }, from, to) };
fun = @(x) { J(x) / N2(x) };
fplot(fun)