[QUE/SM-03016] SM-PROBLEM

 Find the number of energy levels of a particle of mass M in a (a) square box of length L and (b) a cubical box of side L lying between E and $E\,+\,\Delta E$ when the energies are macroscopic. Show that they relate to the corresponding expression obtained classically from $$\int_{E\,\leq\,\Gamma\,\leq\,E+\Delta E}\frac{d^2qd^2p}{h^2}\,;\qquad \int_{E\,\leq\,\Gamma\,\leq\,E+\Delta E}\frac{d^3qd^3p}{h^3} $$

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