2009/07/01 by Petarpa Boonserm, Boonserm, Petarpa · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #gr-qc #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.0907.0045
263 pages; 5 figures; PhD Thesis (Victoria University of Wellington, June 2009)
arxiv created 2009/07/01 · arxiv updated 2009/12/01
This thesis describes the development of some basic mathematical tools of wide relevance to mathematical physics. Transmission and reflection coefficients are associated with quantum tunneling phenomena, while Bogoliubov coefficients are associated with the mathematically related problem of excitations of a parametric oscillator. While many approximation techniques for these quantities are known, very little is known about rigorous upper and lower bounds. In this thesis four separate problems relating to rigorous bounds on transmission, reflection and Bogoliubov coefficients are considered, divided into four separate themes: 1) Bounding the Bogoliubov coefficients; 2) Bounding the greybody factors for Schwarzschild black holes; 3) Transformation probabilities and the Miller--Good transformation; 4) Analytic bounds on transmission probabilities.