  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 {\Psi} or by a certain function g_{F} on phase space canonically
associated with {\Psi}. We study Fermi's function when {\Psi} 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.
