## Definitions and notations

We introduce the following shorthand for the above integral $$\langle \mu | \hat{h}_0 | \mu \rangle = \int \psi_{\mu}^*(x)\hat{h}_0\psi_{\mu}(x)dx,$$ and rewrite Eq. (7) as $$$$\int \Phi^*\hat{H}_0\Phi d\tau = \sum_{\mu=1}^A \langle \mu | \hat{h}_0 | \mu \rangle. \tag{8}$$$$