Classical chaos, quantum mechanics

Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York Springer)... 

Gutzwiller, M. C. Chaos in Classical and Quantum Mechanics Springer-Verlag, New York, 1990. 

MSN.131.1. Prigogine, T. Y. Petrosky, H. H. Hasegawa, and S. Tasaki, Integrability and chaos in classical and quantum mechanics. Chaos, SoUt. Fractals 1, 3-24 (1991). 

MSN. 149. I. Prigogine, Classical and quantum mechanics of unstable dynamical systems, in Proceedings, International Conference on Dynamical Systems and Chaos, Y. Aizawa, S. Saito, and K. Shiraiwa, eds.. World Scientific, Singapore, Vol. 2, 1995. 

MSN. 151.1. Prigogine, Why irreversibility The formulation of classical and quantum mechanics for non-integrable systems, Int. J. Bifurcation and Chaos 5, 3-16 (1995). 

MSN. 155. T. Petrosky and I. Prigogine, Poincare resonances and the extension of classical dynamics, in Special issue Time symmetry breaking in classical and quantum mechanics, Chaos, Solitons and Fractals 7, 441 97 (1996). 

MSN. 159. 1. Prigogine and T. Petrosky, Chaos, time symmetry breaking and the extension of classical and quantum mechanics, in Proceedings, El Escorial course on Foundations of Quantum Physics, Ed. Complutense, Madrid, pp. 183-215. 

But chaos is more than a tool. There are as yet unsolved philosophical problems in its wake. While relativity and quantum mechanics necessitated - and in fact originated from - a careful analysis of the concepts of space, time and measurement, chaos, already on the classical level, forces us to re-think the concepts of determinism and predictability. Thus, classical mechanics could not be further removed from the dusty subject it is usually portrayed as. On the contrary it is at the forefront of modern scientific research. Since path integrals provide a link between classical and quantum mechanics, conceptual and philosophical problems with classical mechanics are bound to manifest themselves on the quantum level. We are only at the beginning of a thorough exploration of these questions. But one fact is established already chaos has a profound in-fiuence on the quantum mechanics of atoms and molecules. This book presents some of the most prominent examples. 

With this section we finish our general survey of chaos in classical and quantum mechanics and turn to a discussion of specific examples of the manifestations of chaos in atomic physics. 

---