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

Abstract

The famous Gordon formula for matrix element n',l|r|n,l-1 is transformed into a new form which can be easily treated when n', n and l are all large. 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 representing a singe Keplerian orbit in terms of a Fourier series of time variable t.