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Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty

Maurice De Gosson
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Abstract

The ground energy level of an oscillator cannot be zero because of Heisenberg's uncertainty principle. We use methods from symplectic topology (Gromov's non-squeezing theorem, and the existence of symplectic capacities) to analyze and extend this heuristic observation to Liouville-integrable systems, and to propose a topological quantization scheme for such systems, thus extending previous results of ours.

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Maurice De Gosson. 2006-02-22. Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty. https://arxiv.org/abs/math-ph/0602055

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