Analytic bounds on transmission probabilities

Details Analytic bounds on transmission probabilities Analytic bounds on transmission probabilities

2009-01-07

arxiv.org/abs/0901.0944v1

Annals of Physics 325 (2010) 1328-1339

Physics

Mathematical Physics

19 pages

Scientific paper

10.1016/j.aop.2010.02.005

We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrodinger equation for some complicated potential whose properties we are trying to investigate in terms of some simpler potential whose properties are assumed known, plus a (possibly large) "shift" in the potential. Doing so permits us to extract considerable useful information without having to exactly solve the full scattering problem.

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