  Eigenvalues and wave functions describing free electron gases in toroidal
shells are determined using a basis set expansion natural to the system
geometry. Couplings between azimuthal and poloidal modes are found to be
appreciable at lower values of ${m_\phi}$, modifying single particle density
distributions within the shells. Thermodynamic state functions are calculated
and contrasted with those of a solid toroidal volume.
