Abstract
Heisenberg's correspondence principle for non-relativistic matrix elements has been generalized: quantal transition amplitudes between strongly coupled states are expressed as Fourier components of integrals over classical trajectories. The new theory reduces to Heisenberg's correspondence principle in particular cases. The theory is applicable whenever the change in quantum number is small compared with the initial quantum number. In these situations it is more comprehensive than both quantal first order perturbation theory and the sudden approximation. Furthermore, compared with standard quantal methods, the evaluation of amplitudes is particularly simple. The theory is worked out for one- and three-dimensional separable systems and the generalization to a system of arbitrary dimension is indicated.