  We study the possible tetraquark interpretation of light scalar meson states
$a_0(980)$, $f_0(980)$, $\kappa$, $\sigma$ within the framework of the
non-relativistic potential model. The wave functions of tetraquark states are
obtained in a space spanned by multiple Gaussian functions. We find that the
mass spectra of the light scalar mesons can be well accommodated in the
tetraquark picture if we introduce a three-body quark interaction in the quark
model. Using the obtained multiple Gaussian wave functions, the decay constants
of tetraquarks are also calculated within the ``fall apart'' mechanism.
