"Sommerfeld model" E = m c^2 (1 + (alpha / (n - k + sqrt(k^2 - alpha^2)))^2)^(-1/2) E = taylor(E,alpha,4) E "Verify equation (1)" check(E == m c^2 (1 - alpha^2 / (2 n^2) - alpha^4 / (2 k n^3) + 3 alpha^4 / (8 n^4))) "ok" E = E - m c^2 "Verify equation (2)" check(E == -alpha^2 m c^2 / (2 n^2) (1 + alpha^2 / n (1 / k - 3 / (4 n)))) "ok" Run