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We present essentially exact solutions of the Schroedinger equation for threefermions in two different spin states with zero-range s-wave interactions underharmonic confinement. Our approach covers spherically symmetric, strictlytwo-dimensional, strictly one-dimensional, cigar-shaped, and pancake-shapedtraps. In particular, we discuss the transition from quasi-one-dimensional tostrictly one-dimensional and from quasi-two-dimensional to strictlytwo-dimensional geometries. We determine and interpret the eigenenergies of thesystem as a function of the trap geometry and the strength of the zero-rangeinteractions. The eigenenergies are used to investigate the dependence of thesecond- and third-order virial coefficients, which play an important role inthe virial expansion of the thermodynamic potential, on the geometry of thetrap. We show that the second- and third-order virial coefficients foranisotropic confinement geometries are, for experimentally relevanttemperatures, very well approximated by those for the spherically symmetricconfinement for all s-wave scattering lengths.

Three s-wave interacting fermions under anisotropic harmonic confinement: Dimensional crossover of energetics and virial coefficients