Statistical Mechanics of One-dimensional Substances I

Abstract

We consider a large number N of molecules which are arranged on a straight line of length l and assume that only the neighbouring pairs interact. As the interaction potential we take each of the three forms shown in fig. 1. The statistical treatment was given for these cases on classical and quantummechanical bases. It was found that these three cases represent the three phases of ordinary substances, gaseous, liquid and solid phases, in an idealized way. The equilibrium of phases was discussed and the fig. 4 was obtained.
The author is indebted to Dr. K. Husimi for kind discussions.