Scattering amplitudes for multi-indexed extensions of solvable potentials

C. L. Ho, Jen-Chi Lee*, R. Sasaki

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Scopus citations

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. Pöschl-Teller and the radial oscillator potentials, has generated the multi-indexed Jacobi and Laguerre polynomials. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials.

Original languageEnglish
Pages (from-to)115-131
Number of pages17
JournalAnnals of Physics
Volume343
DOIs
StatePublished - 1 Apr 2014

Keywords

  • Multi-indexed solvable potential
  • Multiple Darboux transformation
  • Scattering amplitude
  • Shape invariance

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