Some Exactly Solvable Three-Body Problems in One dimension

Abstract

The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body potentials which can be solved algebraically. Analytic expressions for the eigenspectrum and the eigenfunctions are given with and without confinement.

16 pages

References in corpus (2)

• Exchange Operator Formalism for Integrable Systems of Particles
• Spectrum of a spin chain with inverse square exchange

Cited by in corpus (8)

• A Generalized Jaynes-Cummings Hamiltonian and Supersymmetric Shape-Invariance
• Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• An explicit realization of fractional statistics in one dimension
• On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties
• Extending the four-body problem of Wolfes to non-translationally invariant interactions
• Solvable few-body quantum problems
• Exactly solvable $N$-body quantum systems with $N=3^k(k\ge 2)$ in the $D=1$ dimensional space