Transmission probabilities and the Miller-Good transformation

Details Transmission probabilities and the Miller-Good transformation Transmission probabilities and the Miller-Good transformation

2008-08-19

arxiv.org/abs/0808.2516v2

J.Phys.A42:045301,2009

Physics

Mathematical Physics

10 pages. V2: Now 15 pages. Significantly expanded with examples and applications. Matches published version

Scientific paper

10.1088/1751-8113/42/4/045301

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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