  We conisder time-dependent Schr\"odinger systems, which are quantizations of
the Hamiltonian systems obtained from a similarity reduction of the
Drinfeld-Sokolov hierarchy by K. Fuji and T. Suzuki, and a similarity reduction
of the UC hierarchy by T.Tsuda, independently. These Hamiltonian systems
describe isomonodromic deformations for certain Fuchsian systems. Thus, our
Schr\"odinger systems can be regarded as quantum isomonodromic systems. Y.
Yamada conjectured that our quantum isomonodromic systems determine instanton
partition functions in N=2 SU(L) gauge theory.
  The main purpose of this paper is to present integral formulas as particular
solutions to our quantum isomonodromic systems. These integral formulas are
generalizations of the generalized hypergeometric function.
