Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 15.5-3

THE CANONICAL FORMALISM; STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION

Physics — Statistical Mechanics · hypersphere-shell-fraction

Problem

Calculate the fraction of the hypervolume between the radii

0.9r

and

r

for hyperspheres in 1, 2, 3, 4, and 5 dimensions. Similarly for 10, 30, and 50 dimensions.