Analytic bounds on transmission probabilities |
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| Authors: | Petarpa Boonserm Matt Visser |
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| Affiliation: | a Department of Mathematics, Faculty of Science Chulalongkorn University, Phayathai Rd., Pathumwan Bangkok 10330, Thailand
b School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, New Zealand |
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| Abstract: | 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 Schrödinger 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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| Keywords: | Transmission Reflection Bogoliubov coefficients Analytic bounds |
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