Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas
Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas
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不完美玻色气体基态能量的简化方法
DOI：
10.1103/physrev.130.2518
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发表时间：
1963
期刊：
影响因子：
--
通讯作者：
E. Lieb
中科院分区：
文献类型：
--
作者：
E. Lieb
玻色气体基态能量的渐近密度级数中众所周知的前两项，E 0=2πNρa[1+(128/15√π) (ρa 3)1/2]，其中a是电势对的散射长度，通常是通过微扰理论中对无限组图求和得到的。我们在这里展示如何通过初等方法获得相同的级数。我们的方法具有简单和直接的优点。另一个优点是，硬核情况可以在与有限势相同的基础上处理，不需要赝势。事实上，对硬核势的分析比对有限势的分析要简单，就像基本量子力学中的情况一样。在附录中，我们讨论了高密度情况，并表明对于某一类势，博戈留博夫的理论在这个极限上是正确的。因此，博戈留波夫的理论在低密度下永远不会正确，除非引入赝势，但它实际上是一个高密度理论。
The well-known first two terms in the asymptotic density series for the ground-state energy of a Bose gas, E 0=2πNρa[1+(128/15√π) (ρa 3)1/2], where a is the scattering length of the pair potential, is ordinarily obtained by summing an infinite set of graphs in perturbation theory. We show here how this same series may be obtained by elementary methods. Our method offers the advantages of simplicity and directness. Another advantage is that the hard-core case can be handled on the same basis as a finite potential, no pseudopotential being required. In fact, the analysis of the hard-core potential turns out to be simpler than for a finite potential, as is the case in elementary quantum mechanics. In an Appendix we discuss the high-density situation and show that for a certain class of potentials Bogoliubov’s theory is correct in this limit. Thus, Bogoliubov’s theory, which is never correct at low density unless a pseudopotential is introduced, is really a high-density theory.