Blundell Thermal Physics · Problem 19.3

Equipartition of energy

Physics — Statistical Mechanics · equipartition-potential-well-quadratic

Problem

A particle at position

r

is in a potential well

V(r)

given by

V(r) = \frac{A}{r^n} - \frac{B}{r}, \tag{19.28}

where

A

and

B

are positive constants and

n > 2

. Show that the bottom of the well is approximately quadratic in

r

. Hence find the particle's mean thermal energy at temperature

T

above the bottom of the well assuming the validity of the equipartition theorem in this situation.