# Anharmonic Oscillator Heat Capacity

## Homework Statement

Consider the anharmonic potential U(x)=cx2-gx3-fx4 and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is

C=kb[1+(3f/2c2+15g2/8c3)kbT]

## Homework Equations

U(x)=cx2-gx3-fx4
and heat capacity is C=dU/dT

## The Attempt at a Solution

I have used boltzman distrşbution of x as 3g/4c2*kbT and took derivative of U according to T but I could not find the given heat capacity.

G01
Homework Helper
Gold Member

## Homework Statement

Consider the anharmonic potential U(x)=cx2-gx3-fx4 and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is

C=kb[1+(3f/2c2+15g2/8c3)kbT]

## Homework Equations

U(x)=cx2-gx3-fx4
and heat capacity is C=dU/dT

## The Attempt at a Solution

I have used boltzman distrşbution of x as 3g/4c2*kbT and took derivative of U according to T but I could not find the given heat capacity.

OK. But, I can't help you find your mistake if you don't show your calculations.

where did the 3g/4c2*kbT come from?