The Evaluation of Quantum Integrals.

The application of the Wilson-Sommerfeld quantum conditions to a conditionally periodic system with orthogonal coordinates involves the evaluation of an integral of the type J = f(q) dq. (1) The integral is to be extended over a.complete cycle of values of q, which oscillates between two roots of f(q). The sign of the radical is to be the same as that of dq, so that if a and b denote the roots of f(q), the integral can be written j = 2f"ilf(q) dq (2)