Abstract
Exact and closed-form expressions of the particle density and the momentum distribution are derived for a coherent state of a noninteracting Fermi gas, while such a state can be obtained from the ground state in a $d$-dimensional isotropic harmonic trap by modulating the trap frequency and shifting the trap center. The profile of the momentum distribution turns out to be identical in shape with that of the particle density, however, as a manifestation of the Heisenberg uncertainty principle, the dispersion of the distribution increases (decreases) when that of the particle density is decreased (increased). The expressions are also applicable for a sudden and total opening of the trap, and it is shown that, after the opening, the gas has a stationary momentum distribution whose dispersion could be arbitrarily large or small.
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