function e1s=single_gaussian_energy(alph)
alphp=alph;
pe_analytic=-2^(5/2)*(alph.*alphp)^(3/4)./(sqrt(pi)*(alph+alphp));
ke_analytic=3*2^(3/2)*(alph.*alphp)^(7/4)./(alph+alphp)^(5/2);
e1s=pe_analytic+ke_analytic;

