  A compact approximate groundstate of the Kondo problem is introduced. It
consists of four Slater states. The spin up and down states of the localized
d-impurity are paired with two localized s-electron states of opposite spin.
All the remaining s-electron states are rearranged forming two new optimal
orthonormal bases. Through a rotation in Hilbert space the two localized states
(and the rest of the bases) are optimized by minimizing the energy expectation
value. The ground-state energy E and the singlet-triplet excitation energy dE
are calculated numerically. Although the two energies can differ by a factor of
1000, they are obtained simultaneously. The singlet-triplet excitation energy
dE is proportional to exp[-1/2Jg] and quite close to the Kondo temperature
k_BT_K. The cases for anti-ferromagnetic (J>0) and ferromagnetic (J<0) coupling
are investigated.
