  As a first step towards a strong coupling expansion of Yang-Mills theory, the
SU(2) Yang-Mills quantum mechanics of spatially constant gauge fields is
investigated in the symmetric gauge, with the six physical fields represented
in terms of a positive definite symmetric (3 x 3) matrix S. Representing the
eigenvalues of S in terms of elementary symmetric polynomials, the eigenstates
of the corresponding harmonic oscillator problem can be calculated analytically
and used as orthonormal basis of trial states for a variational calculation of
the Yang-Mills quantum mechanics. In this way high precision results are
obtained in a very effective way for the lowest eigenstates in the spin-0
sector as well as for higher spin. Furthermore I find, that practically all
excitation energy of the eigenstates, independently of whether it is a
vibrational or a rotational excitation, leads to an increase of the expectation
value of the largest eigenvalue <\phi_3>, whereas the expectation values of the
other two eigenvalues, <\phi_1> and <\phi_2>, and also the component <B_3> =
g<\phi_1\phi_2> of the magnetic field, remain at their vacuum values.
