  We solve the Schr\"{o}dinger equation for an arbitrary one-dimensional
potential energy to calculate the transmission coefficient in the fission
channel of compound nucleus reactions. We incorporate the calculated
transmission coefficients into the statistical Hauser-Feshbach model
calculation for neutron-induced reactions on $^{235,238}$U and $^{239}$Pu. The
one-dimensional model reproduces the evaluated fission cross section data
reasonably well considering the limited number of model parameters involved. A
resonance-like structure appears in the transmission coefficient for a
double-humped fission barrier shape that includes an intermediate well, which
is understood to be a quantum mechanical effect in the fission channel. The
calculated fission cross sections for the neutron-induced reactions on
$^{235,238}$U and $^{239}$Pu all exhibit a similar structure.
