势场中理想气体粒子分布规律

Particle distribution law of ideal gases in a potential field

应用统计力学的方法,首先证明了玻耳兹曼分布律完全符合统计力学中麦克斯韦-玻耳兹曼统计法,说明了玻耳兹曼分布律与各种势场中的理想气体粒子存在的空间维数和遵从何种能谱无关。然后进一步推证了遵从玻色-爱因斯坦和费米-狄拉克统计法的理想气体粒子处在各种势场中按势能的分布规律,其结论为粒子数密度是势能的幂级数函数。并且应用计算机模拟仿真手段绘制出势场中理想玻色和费米气体粒子按势能分布向经典粒子按势能分布的过渡曲线。由此可以证明玻耳兹曼分布规律只是玻色和费米分布规律的一级近似,所以后者才是处在势场中理想气体粒子的一般性的分布规律。

With the aid of statistical mechanics, we firstly prove that the Maxwell - Boltzman distribution formula of the ideal gas particles is in full consistent with the M-B statistics in statistical mechanics, and account for its availability in various potential fields, irrelevant to the dimensions of the space where the gas exists and to their energy spectrum. We then further derived the distribution law of B-E and F-D ideal gas in a potential field, expressed in the form of a power series in potential energy. Applying computer simulation method, we plotted the distribution curves of the ideal B-E and F-D gas in a potential field successively approaching the distribution curve of the classical particles in the same field. So it turns out that the Boltzman distribution law is only the first order approximation of the Bose or Fermi distribution. We can say it is the latter that is the general distribution law of ideal gas particle in a potential field.