R.K. Pathria in his book Statistical Mechanics has written that the volume of a $3N$-dimensional hypershell, bounded by hyper spheres of radii $$\sqrt{2m(E+\tfrac12\Delta)}\; \text{and}\; \sqrt{2m(E-\tfrac12\Delta)}$$ for $\Delta\ll E$, is almost equal to $\Delta (m/2E)^{\frac12}$ multiplied by the surface area of a $3N$-dimensional hypersphere of radius $\sqrt{2mE}$. Could you explain to me why?
2026-04-18 18:08:13.1776535693
The volume of a 3N-dimensional hypershell
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