
\sect{Pressure in a box with $V(x)$ potenial}

A particle is confined by hard walls to move inside a box $[0,L]$. 
There is an added external potential $U(x)$.  
Find the force ("Pressure") on the wall at ${x=L}$.
 
\Dn

(1) The short way - evalute the density of the particles 
in the vicinity of the wall, and assume that the pressure 
there is the same as that of an ideal gas.
 
\Dn

(2) The long way - using the Virial theorem relate the force 
at ${x=L}$ to the expectation function of $xU'(x)$.

\Dn

(3) Explain why the Virial based derivation gives
the force on the $x=L$ and not on the $x=0$ wall. 
  
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