Improvement of variational approach in an interacting two-fermion system

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

中国物理B ›› 2015, Vol. 24 ›› Issue (8): 86701-086701.doi: 10.1088/1674-1056/24/8/086701

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇下一篇

Improvement of variational approach in an interacting two-fermion system

刘彦霞, 叶君, 李源远, 张云波

Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006, China

收稿日期:2015-04-14 修回日期:2015-05-06 出版日期:2015-08-05 发布日期:2015-08-05
基金资助:
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).

Improvement of variational approach in an interacting two-fermion system

Liu Yan-Xia (刘彦霞), Ye Jun (叶君), Li Yuan-Yuan (李源远), Zhang Yun-Bo (张云波)

Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006, China

Received:2015-04-14 Revised:2015-05-06 Online:2015-08-05 Published:2015-08-05
Contact: Zhang Yun-Bo E-mail:ybzhang@sxu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Bethe-ansatz, variational approaches, exact solution

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.

Key words: Bethe-ansatz, variational approaches, exact solution

中图分类号: (Degenerate Fermi gases)

67.85.Lm

03.75.Ss (Degenerate Fermi gases) 02.30.Ik (Integrable systems)

刘彦霞, 叶君, 李源远, 张云波. Improvement of variational approach in an interacting two-fermion system[J]. 中国物理B, 2015, 24(8): 86701-086701.

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[J]. Chin. Phys. B, 2015, 24(8): 86701-086701.

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Improvement of variational approach in an interacting two-fermion system

Improvement of variational approach in an interacting two-fermion system

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