Solution of the Dirac equation in a deformed bag

The energy levels of massless quarks confined in a deformed cavity (bag) are calculated by the Dirac equation subject to the MIT-bag boundary condition. The levels up to $m^{\pi }={\frac{7}{2}}^{\pm }$ are given over a wide range of deformations of the ellipsoid of revolution. The deformation dependence of these energies indicates that some excited baryon resonances may be deformed, in agreement with other reported calculations.