= Quadratic-boson heat-capacity coefficient
{title2=$C/V=5\Gamma(5/2)\zeta(5/2)k_B^{5/2}T^{3/2}/(8\pi^2\hbar^3\alpha^{3/2})$}
One isotropic three-dimensional bosonic branch with dispersion $\epsilon=\alpha p^2$ and zero <chemical potential> has <density of states> per <volume> $\sqrt\epsilon/(4\pi^2\hbar^3\alpha^{3/2})$. Integrating its Bose-Einstein <energy> and differentiating <temperature> gives the title coefficient. Identical independent branches multiply it by their number. Thus a measured $T^{3/2}$ coefficient fixes branch multiplicity divided by $\alpha^{3/2}$, not a dispersion coefficient independent of that counting convention. A gap or low-dimensional spectrum changes the asymptotic law.
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