On the Fermi Function of Squeezed Coherent States

Fermi observed 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 $\Psi$. In this Note we study we study Fermi's function when $\Psi$ is a squeezed coherent state. We relate it with the Wigner transform of $\Psi$, thus generalising a previous observation of Benenti and Strini. We show that the symplectic capacity of the phase space ellipsoid $g_{F}(x,p)\leq0$ is bounded by $h/2$ and $nh/2$ (n the number of degrees of freedom).