Eigenfunctions, eigenvalues, and time evolution of finite, bounded, undriven, quantum systems are not chaotic

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Abstract
We prove here that the eigenvalues, eigenfunctions, and time evolutions for a broad class of spatially bounded, finite particle number, undriven, quantum systems can be computed by algorithms containing logarithmically less information than the quantities themselves. Algorithmic complexity theory asserts that such quantal systems are nonchaotic. These results are shown to be valid independent of the size of system parameters such as mass or Planck’s constant, provided they are not set equal to zero or infinity. However, rather than confronting quantum mechanics with classical mechanics via the correspondence principle, we suggest a direct comparison of quantum mechanics with macroscopic laboratory reality. Specifically, we here propose the double pendulum—a simple, two-degree-of-freedom, macroscopic system exhibiting a transition to chaos as its amplitude increases—as a model suitable for testing whether a nonchaotic quantum mechanics can accurately predict laboratory observation. Neither theory nor experiment appears to offer insurmountable difficulties to the performance of this comparison.

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