Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 15.2-2

THE CANONICAL FORMALISM; STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION

Physics — Statistical Mechanics · einstein-model-mean-quantum-number

Problem

Obtain an equation for the mean quantum number

\bar{n}

of an Einstein oscillator as a function of the temperature. Calculate

\bar{n}

for

k_BT/\hbar\omega_0 = 0, 1, 2, 3, 4, 10, 50, 100

(ignore the physical reality of melting of the crystal!).