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arXiv · 1301.0923

Fermi's Trick and Symplectic Capacities: A Geometric Picture of Quantum States

Maurice A. de Gosson·Serge M. de Gosson
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Abstract

We extend the notion of quantum blob studied in previous work to excited states of the generalized harmonic oscillator in n dimensions. This extension is made possible by Fermi's observation in 1930 that the state of a quantum system may be defined in two different (but equivalent) ways, namely by its wavefunction Ψ or by a certain function g_{F} on phase space canonically associated with Ψ. We study Fermi's function when Ψ is a Gaussian (generalized coherent state). A striking result is that we can use the Ekeland--Hofer symplectic capacities to characterize the Fermi functions of the excited states of the generalized harmonic oscillator, leading to new insight on the relationship between symplectic topology and quantum mechanics.

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Maurice A. de Gosson, Serge M. de Gosson. 2013-01-05. Fermi's Trick and Symplectic Capacities: A Geometric Picture of Quantum States. https://arxiv.org/abs/1301.0923

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