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\sect{Gas in $x^2$ box potential}

Coansider ${N}$ classical particles in a potential
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\begin{displaymath}
V \left(x,y,z\right)=\left\{ \begin{array}{ll}
\frac{1}{2}ax^{2} & \textrm{$0<x, \ 0<y<L, \ 0<z<L$} \\
\infty & \textrm{else}
\end{array} \right.
\end{displaymath}
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Calculate the partition function and detirve from it an expression 
for the pressure on the wall at ${x=0}$. Note that for this purpose 
you have to re-define the potential, such that it would depend 
on a paramter $X$ that describes the poition of the wall.

Show that the result for the perssure can be optionally obtained  
by assuming that the pressure is the same as that of an ideal gas.
For this purpose evalute the density of the particles in the vicinity of the wall. 

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