Transmission probabilities and the Miller-Good transformation
Petarpa Boonserm (Victoria University of Wellington), Matt Visser, (Victoria University of Wellington)
TL;DR
This paper introduces a generalized bound on quantum transmission probabilities using the Miller-Good transformation, expanding the analysis of particle transmission and production in quantum systems and black hole physics.
Contribution
It applies the Miller-Good transformation to significantly extend previous bounds on quantum transmission probabilities and greybody factors.
Findings
Derived a more general bound on quantum transmission probabilities
Applied the transformation to black hole greybody factors
Enhanced understanding of particle production in quantum systems
Abstract
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.
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