Improvement of variational approach in an interacting two-fermion system

doi:10.1088/1674-1056/24/8/086701

Abstract A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a one-dimensional (1D) harmonic potential. At the boundaries both the wave function and its first derivative are continuous and the quasi-momentum is determined by a more practical constraint condition which associates two variational parameters. The upper bound of the ground state energy is obtained by applying the variational principle to the expectation value of the Hamiltonian of relative motion on the trial wave function. The resulted energy and wave function show better agreement with the analytical solution than the original proposal.

Keywords: Bethe-ansatz variational approaches exact solution

Received: 14 April 2015
Revised: 06 May 2015
Accepted manuscript online:

PACS:	67.85.Lm	(Degenerate Fermi gases)
	03.75.Ss	(Degenerate Fermi gases)
	02.30.Ik	(Integrable systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11234008 and 11474189), the National Basic Research Program of China (Grant No. 2011CB921601), and the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13076).

Corresponding Authors: Zhang Yun-Bo
E-mail: ybzhang@sxu.edu.cn

Cite this article:

Liu Yan-Xia (刘彦霞), Ye Jun (叶君), Li Yuan-Yuan (李源远), Zhang Yun-Bo (张云波) Improvement of variational approach in an interacting two-fermion system 2015 Chin. Phys. B 24 086701

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