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## Homework Statement

Consider the anharmonic potential U(x)=cx

^{2}-gx

^{3}-fx

^{4}and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is

C=k

_{b}[1+(3f/2c

^{2}+15g

^{2}/8c

^{3})kbT]

## Homework Equations

U(x)=cx

^{2}-gx

^{3}-fx

^{4}

and heat capacity is C=dU/dT

## The Attempt at a Solution

I have used boltzman distrşbution of x as 3g/4c

^{2}*kbT and took derivative of U according to T but I could not find the given heat capacity.