Scattering Amplitudes for Multi-indexed Extensions of Solvable Potentials
Quantum Physics
2015-06-17 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Spectral Theory
Exactly Solvable and Integrable Systems
Abstract
New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method applied to confining potentials, e.g. P\"oschl-Teller and the radial oscillator potentials, has generated the {\em multi-indexed Jacobi and Laguerre polynomials}. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials.
Cite
@article{arxiv.1309.5471,
title = {Scattering Amplitudes for Multi-indexed Extensions of Solvable Potentials},
author = {C. -L. Ho and J. -C. Lee and R. Sasaki},
journal= {arXiv preprint arXiv:1309.5471},
year = {2015}
}
Comments
28 pages, no figures. Acknowledgments revised