量子巨配分函数的洽当导出

2019 , Vol. 38 >Issue 4: 1 - 3

教学研究

量子巨配分函数的洽当导出

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包景东( 1962—) ，男，辽宁瓦房店人，北京师范大学物理学教授，博士，主要从事热力学与统计物理、

收稿日期: 2018-10-30

修回日期: 2018-12-04

网络出版日期: 2019-05-06

基金资助

国家自然科学重点基金( 11735005) 资助

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Alternative derivation of quantum huge partition function

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Received date: 2018-10-30

Revised date: 2018-12-04

Online published: 2019-05-06

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巨配分函数是平衡态统计物理教学的难点问题.目前的教材在量子统计中，先引入这个函数的自然对数，然后根据

它表示的热力学量来说明其正确性，这在逻辑上是不顺畅的.本文从T-μ-V 系统的平均能量、平均粒子数和广义力的定义，用

凑全微分法和不定积分法分别导出了量子巨配分函数，还对选择具有物理意义的自变参量进行了讨论.

关键词： 量子统计; 巨配分函数; 凑全微分法; 不定积分法

包景东 . 量子巨配分函数的洽当导出[J]. 大学物理, 2019 , 38(4) : 1 -3 . DOI: 10.16854 /j.cnki.1000-0712.180958

The huge partition function is a difficult problem in teaching equilibrium statistical physics. In the

present textbooks，the logarithm of huge partition function is introduced firstly，and then the correctness of this formula

producing thermodynamics functions is affirmed. However，this is not order in the logic. Based on the average

energy，the average particle number and the generalized force of the T-μ-Vsystem，this paper derives the quantum

huge partition function by using collecting full differential method and unfined integral method，respectively. The

physical mean of what variables regarded to two independent parameters is discussed.

Key words： quantum statistics; huge partition function; collecting full differential method; idefinite integration

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