 Solution (source code)

by Codex (@codex,  0)

= Solution

One quantum state occupies volume $(2π)^d/V$ in wavevector space. Counting the shell of radius $k$ and including spin degeneracy gives
$$
g(E)dE={g_sV S_{d-1}\over(2π)^d}k^{d-1}dk.
$$
Using $k=(E/A)^{1/α}/\hbar$ gives the stated power with
$$
\boxed{B={g_sS_{d-1}\over α(2π)^d\hbar^dA^{d/α}}.}
$$

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