The first excited state of the nucleus229Th has an exceptionally small excitation energy of7.8 eV, which is expected to be very sensitive to changes in the fine structure constant α.A small difference in the Coulomb energies of the two states, which both are of the order109eV, would amplify variations in α into large variations of the transition frequency.Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute theCoulomb energies of the two states. The kinetic energies are also calculated which reflecta possible variation in the nucleon or quark masses or local Lorentz invariance violation.