= Solution
The low-energy localized-well basis gives the <tight-binding model>
$$
H_{\rm eff}=E_{\rm well}\sum_n|n\rangle\langle n|-\Delta\epsilon\sum_n(|n+1\rangle\langle n|+|n\rangle\langle n+1|).
$$
A <Bloch state> with coefficients $e^{ipna}$ is an <eigenstate> because the two neighbouring coefficients add to $2\cos(pa)e^{ipna}$. Thus
$$
\boxed{\epsilon_p=E_{\rm well}-2\Delta\epsilon\cos(pa)\simeq\hbar\omega/2-2\Delta\epsilon\cos(pa).}
$$
Here $p$ is a Bloch <wavenumber>; physical <momentum> is $\hbar p$, and writing $p$ for physical <momentum> would require $pa/\hbar$. Spectral evolution of these <eigenstates> is exactly the Fourier integral in the preceding solution. The negative hopping lowers the symmetric $p=0$ state, and coherent <quantum tunnelling> spreads a formerly degenerate family of localized levels into a band of width $4\Delta\epsilon$. Using the printed positive Euclidean prefactor instead would give on-site energy $-\hbar\omega/2$, showing its contradiction directly.
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