Statistical Mechanics · Problem 1.8

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · harmonic-oscillator-quasiparticles-microstate-count

Problem

Consider a system of quasi-particles whose energy eigenvalues are given by

\varepsilon(n) = nh\nu; \quad n = 0, 1, 2, \ldots

Obtain an asymptotic expression for the number

\Omega

of this system, for a given number

N

of the quasi-particles and a given total energy

E

. Determine the temperature

T

of the system as a function of

E/N

and

h\nu

, and examine the situation for which

E/(Nh\nu) \gg 1