2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215224Transmission 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.10 pages. V2: Now 15 pages. Significantly expanded with examples and applications. Matches published versionMathematical PhysicsHigh Energy Physics - TheoryQuantum Physicstext