Some general bounds for one-dimensional scattering

One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this paper I establish some very general bounds for reflection and transmission coefficients for one-dimensional potential scattering. Equivalently, these results may be phrased as general bounds on the Bogolubov coefficients or statements about the transfer matrix. A similar analysis can be provided for the parametric change of frequency of a harmonic oscillator. A number of specific examples are discussed. In particular I provide a general proof that sharp step function potentials always scatter more effectively than the corresponding smoothed potentials. The analysis also serves to collect together and unify what would other-wise appear to be quite unrelated results. [S1050-2947(99)08101-9].