I. First Indication of The Generalization of The Correspondence Principle

Adam J. Makowski

Several formulations of the correspondence principle, including both the historical and contemporary ones, are presented and critically reviewed.

G. Fáy

Ian Colin Percival, D Richards

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.

Handel, P. H.

Since the first experiments of the quantum modulation of electron beams by lasers with a crystal as medium in the interaction area ~d1warz-Hora effect) were reported, extensive theoretical studies were performed.A very detaile/ rLproduction of these experiments was achieved (by Andrick and Langhans, further by Weingartshofer et al) where the medium in the interaction area was a gas.The initial clarification of the experiments with crystal as a quantum phenomenon is using a threshold defining a correspondence principle for electromagnetic interaction.Recent experiments by Weingartshofer et al independently confirm this correspondence principle.For two other experiments the ranges of quantum and classical regimes are elaborated to explain the basically differing character of observations.The discussion of the coherence for matter waves is followed up from the beginning of the Schwarz-Hora effect including developments reviewed by Hawkes and indicating further generalizations by the Hanbury-Brown/ Twiss effect.A consequent generalization of the scattering theory of the quantum modulation is presented based on a Green's function solution which results in the fact that far-field superpositions only lead to interferences.The problems of the re-emission of photons from quantum modulated electron beams is discussed and experiments on indirect observations of the phenomena in microwave amplification and in the 1/f noise Handel effect are reported.In the last case. . the self-interaction of electrons are involved in the Handel effect.A further second-quantised derivation and the coherent state Handel effect is presented.

J. B. Delos, M. L. Du

The general correspondence principle specifies a relationship between wave functions and families of trajectories. For bounded systems with regular trajectories, this general correspondence principle leads to the principle of quantization of action. The general principle also leads to a correspondence principle for finite-resolution spectra: oscillation in the average density of states, or in the average oscillator strength as a function of energy, are connected to periodic or to closed orbits. This principle holds independently or whether classical trajectories are orderly or chaotic.>