Chin. Phys. Lett.  2009, Vol. 26 Issue (12): 120505    DOI: 10.1088/0256-307X/26/12/120505
GENERAL |
Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction
MA Zhong-Qi1, C. N. Yang2,3
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 1000492Institute for Advanced Study, Tsinghua University, Beijing 1000843Institute of Theoretical Physics, The Chinese University of Hong Kong, Hong Kong
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MA Zhong-Qi, C. N. Yang 2009 Chin. Phys. Lett. 26 120505
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Abstract Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.
Keywords: 05.30.Fk      67.85.-d      03.75.Hh     
Received: 02 September 2009      Published: 27 November 2009
PACS:  05.30.Fk (Fermion systems and electron gas)  
  67.85.-d (Ultracold gases, trapped gases)  
  03.75.Hh (Static properties of condensates; thermodynamical, statistical, and structural properties)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/26/12/120505       OR      https://cpl.iphy.ac.cn/Y2009/V26/I12/120505
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MA Zhong-Qi
C. N. Yang
[1] Olshanii M 1998 Phys. Rev. Lett. 81 938 Bloch I et al 2008 Rev. Mod. Phys. 80 885
[2]Guan L M et al 2009 Phys. Rev. Lett. 102 160402
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[4]Yang C N 2009 Chin. Phys. Lett. 26 120504. Wewill follow the notation of this paper.
[5]Lieb E and Mattis D 1962 Phys. Rev. 125 164
[6]Girardeau M D and Minguzzi A 2007 Phys. Rev. Lett. 99 230402
[7]Gradshteyn I S and Ryzhik I M 1980 Table of Integrals,Series, and Products (New York: Academic)
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