The hydrogen atom's quantum-to-classical correspondence in Heisenberg's correspondence principle

The famous Gordon formula for matrix element <n', l \r \n, l-1 > is transfo rmed into a new form which can be easily treated when n', n and l are all l arge. Then its asymptotic expression is derived which turns out to be that obtained from Heisenberg's correspondence principle. Finally, its classical limit form is used to construct classical quantities x, y and z representi ng a singe Keplerian orbit in terms of a Fourier series of time variable t.