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\sect{What does it mean particle in a 2D box}

What is two dimensional gas?

Given gas in a box with dimensions ${\left(L<<L\right)
L\times L\times L}$. \\
Determine what are the energies of the uniparticle states. Show that
there's an energy range ${0<E<E_{max}}$ where it's possible to
relate  the gas as a gas in a ${2-D}$ space with a states density
function
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\[g\left(E\right)=A \frac{m}{2\pi} \,\,\,\,0\leq E\,\,\,\,
\left(A\equiv L^{2}\right)\]
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