"Hydrogen atom statistics 1" psi = exp(-r / a0) / sqrt(pi a0^3) "Verify integrals" f = 4 pi psi conj(psi) r^2 F = 4 / a0^3 exp(-2 r / a0) (-1/2 a0 r^2 - 1/2 a0^2 r - 1/4 a0^3) check(integral(f,r) == F) check(d(F,r) == f) Pr = 1 - (2 a^2 / a0^2 + 2 a / a0 + 1) exp(-2 a / a0) check(defint(f,r,0,a) == Pr) "ok" "Probability inside Bohr radius" float(eval(Pr, a, a0)) Run