  Transmission through a potential barrier, and the related issue of particle
production from a parametric resonance, are topics of considerable general
interest in quantum physics. The authors have developed a rather general bound
on quantum transmission probabilities, and recently applied it to bounding the
greybody factors of a Schwarzschild black hole. In the current article we take
a different tack -- we use the Miller-Good transformation (which maps an
initial Schrodinger equation to a final Schrodinger equation for a different
potential) to significantly generalize the previous bound.
