Correspondence identities II. The Bohr-Sommerfeld identity for the hydrogen atom

Abstract

The Bohr-Sommerfeld identity between the hydrogen energy levels given by the old quantum theory and the actual energy levels is explained. The quantum-dynamical solution of the hydrogen-like problem is obtained for bound states in terms of sums over classical paths using the symmetric representation of Fock. The classical analogue of the Fock theory of the hydrogen atom is discussed. Schwinger's expression for the Green function is obtained in a new form.