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

2013/01/05 by Maurice A. de Gosson, de Gosson, Maurice A., Serge M. de Gosson +1
Physics and Astronomy · #Quantum Mechanics and Applications #Mechanical and Optical Resonators #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1301.0923

Abstract

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

Citations

• The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

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