Anharmonic Oscillator Heat Capacity

nyvane
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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.
 
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nyvane said:

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?
 

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