1. Perturbation theory at large order is to be pointed out as a very active field of research. As a readable, very authoritative reference in this broad area we limit ourselves to quote theProceedings of the International Workshop on Perturbation Theory at Large Order, appeared inInt. J. Quantum Chem.,21, issue No. 1 (1982). A few references which are more relevant to the specific content of our paper are the following:a)F. V. Bunkin andI. I. Tugov:Phys. Rev. A,8, 601 (1973);b)F. H.M. Faisal:Nuovo Cimento B,33, 775 (1976);c)P. Lambropoulos: inAdvances in Atomic Molecular Physics, edited byD. R. Bates andB. Bederson, Vol.12 (Academic Press, New York, N. Y., 1976), p. 87;d)S. Yeh andP. Stehle:Phys. Rev. A,15, 213 (1977);e)L. Mower:Phys. Rev. A,22, 882 (1980);f)Y. Gontier, N. K. Rahman andM. Trahin:Nuovo Cimento D,4, 1 (1984).
2. The application of the time-honoured gauge-invariance principle in quantum mechanics has stirred a lot of attention in recent years, especially in the context of deriving correct transition probabilities between quantum states. Here is a selection of relevant papers:K.-H. Yang:Ann. Phys. (N. Y.),101, 62 (1976);C. Cohen-Tannoudji, B. Diu andF. Laloë:Quantum Mechanics (John Wiley and Sons, New York, N. Y., 1977), p. 315;J. J. Forney, A. Quattropani andF. Basani:Nuovo Cimento B,37, 78 (1977);D. H. Kobe:Phys. Rev. Lett. 40, 538 (1978);D. H. Kobe andA. L. Smirl:Am. J. Phys.,46, 624 (1978);C. Leubner andP. Zoller:J. Phys. B,13 3613 (1980);C. Leubner:Am. J. Phys.,49, 738 (1981);Y. Aharonov andC. K. Au:Phys. Lett. A,86, 269 (1981);K.-H. Yang:Phys. Lett. A,92, 71 (1982);J. Bergou:J. Phys. B,16, L647 (1983).
3. There exists a real plenty of material scattered through the literature. We limit here ourselves to quote one book and three collections of papers appeared in the past few years:M. H. Mittleman:Introduction to the Theory of Laser-Atom Interactions (Plenum Press, New York, N. Y., 1982);Photon-Assisted Collisions and Related Topics, edited byN. K. Rahman andC. Guidotti (Harwood Acad. Publ., Chur, London, New York, N. Y., 1982);Collisions and Half-Collisions with Lasers, edited byN. K. Rahman andC. Guidotti (Harwood Acad. Publ., Chur, London, New York, N. Y., 1984);J. Phys. (Paris) Colloq.,46 C1 (1985).
4. I. J. Berson:J. Phys. B.,8, 3078 (1975);b)T. T. Wu: inResonances-Models and Phenomena, Lecture Notes in Physics, Vol.211, edited byS. Albeverio, L. S. Ferreira andL. Streit (Springer, Berlin, 1984), p. 293.
5. G. P. Arrighini, F. Biondi andC. Guidotti:J. Phys. B, to appear.