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\sect{Charged Bose gas in box with potential difference}
Consider ${N}$ bozons with mass ${\mathsf{m}}$, positive charge
${e}$ and spin ${0}$. The particles are in a tank in thermic
equilibrium, and temperature ${T}$. The tank has two zones ${A}$
and ${B}$, The volume of each zone is ${L^{3}}$.A battery creates
potential difference ${V}$ between the zones. The potential in
every zone is homogenous.
Find the condition on ${N}$, so if ${V=0}$ then there's no
condensation, but if ${V=\infty}$ then there's condensation.
answer: ${L^{3}\zeta\left(\frac{3}{2}\right)\cdot
\left(\frac{mT}{2\pi}\right)^{\frac{3}{2}}