Abstract
Quantum mechanics was first developed and tried out on a few integrable systems, such as the harmonic oscillator, the hydrogen atom, and the electron in a rectangular box. In spite of the conceptual differences between the classical and the quantal regimie, the mathematical connection is quite close in these special cases. Some of the relevant methods can be carried over into systems with soft chaos, and seem to yield reasonable results, as if quantum mechanics were capable of riding smoothly over the rough spots in classical mechanics.
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© 1990 Springer Science+Business Media New York
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Gutzwiller, M.C. (1990). The Quantization of Integrable Systems. In: Chaos in Classical and Quantum Mechanics. Interdisciplinary Applied Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0983-6_15
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DOI: https://doi.org/10.1007/978-1-4612-0983-6_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6970-0
Online ISBN: 978-1-4612-0983-6
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