"Zeeman effect" E(n,l,j,mj) = E0 / n^2 (1 + alpha^2 / n^2 (n / (j + 1/2) - 3/4)) + gJ(l,j) mj muB B gJ(l,j) = 1 + (j (j + 1) - l (l + 1) + 3/4) / (2 j (j + 1)) check(E(2,1,3/2,3/2) == E0/4 (1 + 1/16 alpha^2) + 2 muB B) check(E(2,1,3/2,-3/2) == E0/4 (1 + 1/16 alpha^2) - 2 muB B) check(E(2,1,3/2,1/2) == E0/4 (1 + 1/16 alpha^2) + 2/3 muB B) check(E(2,1,3/2,-1/2) == E0/4 (1 + 1/16 alpha^2) - 2/3 muB B) check(E(2,1,1/2,1/2) == E0/4 (1 + 5/16 alpha^2) + 1/3 muB B) check(E(2,1,1/2,-1/2) == E0/4 (1 + 5/16 alpha^2) - 1/3 muB B) check(E(2,0,1/2,1/2) == E0/4 (1 + 5/16 alpha^2) + muB B) check(E(2,0,1/2,-1/2) == E0/4 (1 + 5/16 alpha^2) - muB B) "ok" -- CODATA Internationally recommended 2022 values -- https://physics.nist.gov/cuu/Constants/ alpha = 7.2973525643 10^(-3) c = 299792458.0 meter / second e = 1.602176634 10^(-19) coulomb me = 9.1093837139 10^(-31) kilogram mp = 1.67262192595 10^(-27) kilogram joule = kilogram meter^2 / second^2 eV = 1/e coulomb / joule "eV" mu = me mp / (me + mp) E0 = -mu c^2 alpha^2 / 2 eV E0 Run