On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties

Abstract

We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the oscillator potential. We also present exact scattering solution of a new family of three-body problems in one dimension.

10 pages, LaTeX, no figure

References in corpus (2)

• Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators
• Exact Solution of a Class of Three-Body Scattering Problems in One dimension

Cited by in corpus (5)

• Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd $k$
• Rationally-extended Dunkl oscillator on the line
• Poeschl-Teller paradoxes
• Exactly solvable three-body Calogero-type model with translucent two-body barriers
• Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane