(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Having a unidemsional array of N oscillators with same frequency w and with an anharmonic factor [tex]ax^4[/tex] where 0 < a << 1

Calculate, up to the first order of a, the partition function.

2. Relevant equations

For one oscillator

[tex]Z=\frac{1}{h}\int{e^{-\beta(p^2/2m+1/2mw^2x^2+ax^4)}dpdx}[/tex]

3. The attempt at a solution

Tried to

[tex]Z=\frac{K'}{h}\int{e^{\frac{-\beta*mw^2x^2}{2}(1+\frac{2a}{mw^2}x^2))}dpdx}[/tex]

and I guess I can approximate [tex](1+bx^2)[/tex] to something ... but I know more or less the solution and I can't figure out how to reach it.

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# Homework Help: Partition function of classical oscillator with small anharmonic factor

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