ON THE SHAPE DEPENDENCE OF THE TRANSLATIONAL PARTITION-FUNCTION

The partition functions q of a particle moving in some two- and three-dimensional potentials with infinite barrier height were examined in order to investigate the influence of shape on the translational partition function. The partition functions of the square, rectangle, isosceles right triangle, equilateral triangle, circle and sphere were evaluated numerically or by suitable analytical methods. The results were fitted as empirical polynomials of square and cube roots of the classical limit kappa of the partition function. The empirical relations were shown to hold over a wide range of kappa . Their coefficients were compared with asymptotic expansions.