Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches

Abstract

In this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground state energy of the relative motion of a system of two fermions with spin up and down interacting via a delta-function potential in a 1D harmonic trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.

8 pages, 2 figures

References in corpus (4)

• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
• Ground State Properties of a Tonks-Girardeau Gas in a Split Trap
• Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization

Cited by in corpus (3)

• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Dynamical realization of magnetic states in a strongly interacting Bose mixture
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction